diff --git a/src/main/java/mathlearning/App.java b/src/main/java/mathlearning/App.java
new file mode 100644
index 0000000..0e2ff2d
--- /dev/null
+++ b/src/main/java/mathlearning/App.java
@@ -0,0 +1,24 @@
+package mathlearning;
+
+import mathlearning.service.UserService;
+import mathlearning.ui.LoginFrame;
+
+import javax.swing.*;
+
+public class App {
+    public static void main(String[] args) {
+        // 设置UI风格
+        try {
+            UIManager.setLookAndFeel(UIManager.getCrossPlatformLookAndFeelClassName());
+        } catch (Exception e) {
+            e.printStackTrace();
+        }
+
+        // 启动应用程序
+        SwingUtilities.invokeLater(() -> {
+            UserService userService = new UserService();
+            LoginFrame loginFrame = new LoginFrame(userService);
+            loginFrame.setVisible(true);
+        });
+    }
+}
diff --git a/src/main/java/mathlearning/model/User.java b/src/main/java/mathlearning/model/User.java
new file mode 100644
index 0000000..57b7887
--- /dev/null
+++ b/src/main/java/mathlearning/model/User.java
@@ -0,0 +1,41 @@
+package mathlearning.model;
+
+import java.time.LocalDateTime;
+
+public class User {
+    private String username;
+    private String email;
+    private String passwordHash;
+    private LocalDateTime registrationDate;
+    private String verificationCode;
+    private boolean verified;
+
+    public User() {}
+
+    public User(String email, String passwordHash, String verificationCode) {
+        this.email = email;
+        this.passwordHash = passwordHash;
+        this.verificationCode = verificationCode;
+        this.verified = false;
+        this.registrationDate = LocalDateTime.now();
+    }
+
+    // Getters and setters
+    public String getEmail() { return email; }
+    public void setEmail(String email) { this.email = email; }
+
+    public String getPasswordHash() { return passwordHash; }
+    public void setPasswordHash(String passwordHash) { this.passwordHash = passwordHash; }
+
+    public String getVerificationCode() { return verificationCode; }
+    public void setVerificationCode(String verificationCode) { this.verificationCode = verificationCode; }
+
+    public boolean isVerified() { return verified; }
+    public void setVerified(boolean verified) { this.verified = verified; }
+
+    public LocalDateTime getRegistrationDate() { return registrationDate; }
+    public void setRegistrationDate(LocalDateTime registrationDate) { this.registrationDate = registrationDate; }
+
+    public String getUsername() { return  username; }
+    public void setUsername(String username) {this.username = username; }
+}
diff --git a/src/main/java/mathlearning/service/EmailService.java b/src/main/java/mathlearning/service/EmailService.java
new file mode 100644
index 0000000..86f5b0d
--- /dev/null
+++ b/src/main/java/mathlearning/service/EmailService.java
@@ -0,0 +1,57 @@
+package mathlearning.service;
+
+import javax.mail.*;
+import javax.mail.internet.*;
+import java.util.Properties;
+
+public class EmailService {
+    private final String host;
+    private final String port;
+    private final String username;
+    private final String password;
+    private final boolean auth;
+
+    public EmailService(String host, String port, String username, String password, boolean auth) {
+        this.host = host;
+        this.port = port;
+        this.username = username;
+        this.password = password;
+        this.auth = auth;
+    }
+
+    public boolean sendVerificationCode(String toEmail, String verificationCode) {
+        try {
+            Properties props = new Properties();
+            props.put("mail.smtp.host", host);
+            props.put("mail.smtp.port", port);
+            props.put("mail.smtp.auth", auth);
+            props.put("mail.smtp.starttls.enable", "true");
+
+            Session session = Session.getInstance(props, new Authenticator() {
+                @Override
+                protected PasswordAuthentication getPasswordAuthentication() {
+                    return new PasswordAuthentication(username, password);
+                }
+            });
+
+            Message message = new MimeMessage(session);
+            message.setFrom(new InternetAddress(username));
+            message.setRecipients(Message.RecipientType.TO, InternetAddress.parse(toEmail));
+            message.setSubject("数学学习软件 - 注册验证码");
+
+            String emailContent = "尊敬的用户：\n\n" +
+                    "您的注册验证码是：" + verificationCode + "\n\n" +
+                    "该验证码有效期为10分钟。\n\n" +
+                    "如果您没有注册本软件，请忽略此邮件。\n\n" +
+                    "数学学习软件团队";
+
+            message.setText(emailContent);
+
+            Transport.send(message);
+            return true;
+        } catch (Exception e) {
+            e.printStackTrace();
+            return false;
+        }
+    }
+}
diff --git a/src/main/java/mathlearning/service/UserService.java b/src/main/java/mathlearning/service/UserService.java
new file mode 100644
index 0000000..f239562
--- /dev/null
+++ b/src/main/java/mathlearning/service/UserService.java
@@ -0,0 +1,175 @@
+package mathlearning.service;
+
+import com.fasterxml.jackson.databind.ObjectMapper;
+import com.fasterxml.jackson.datatype.jsr310.JavaTimeModule;
+import mathlearning.model.User;
+import at.favre.lib.crypto.bcrypt.BCrypt;
+
+import java.io.File;
+import java.io.IOException;
+import java.time.LocalDateTime;
+import java.util.*;
+import java.util.concurrent.ConcurrentHashMap;
+
+public class UserService {
+    private static final String USERS_FILE = "data/users.json";
+    private static final long VERIFICATION_CODE_EXPIRY_MINUTES = 10;
+
+    private Map<String, User> users;
+    private Map<String, LocalDateTime> verificationCodeTimestamps;
+    private ObjectMapper objectMapper;
+
+    public UserService() {
+        this.users = new ConcurrentHashMap<>();
+        this.verificationCodeTimestamps = new ConcurrentHashMap<>();
+        this.objectMapper = new ObjectMapper();
+        objectMapper.registerModule(new JavaTimeModule());
+        loadUsers();
+    }
+
+    private void loadUsers() {
+        try {
+            File file = new File(USERS_FILE);
+            if (file.exists() && file.length() > 0) {
+                User[] userArray = objectMapper.readValue(file, User[].class);
+                for (User user : userArray) {
+                    users.put(user.getEmail(), user);
+                }
+                System.out.println("成功加载 " + userArray.length + " 个用户");
+            } else {
+                saveUsers();
+                System.out.println("创建新的用户数据文件");
+            }
+        } catch (IOException e) {
+            System.err.println("加载用户数据失败: " + e.getMessage());
+            backupAndRecreateFile();
+        }
+    }
+
+    private void backupAndRecreateFile() {
+        try {
+            File file = new File(USERS_FILE);
+            if (file.exists()) {
+                File backup = new File(USERS_FILE + ".bak." + System.currentTimeMillis());
+                file.renameTo(backup);
+                System.err.println("损坏的文件已备份为: " + backup.getName());
+            }
+            saveUsers();
+            System.out.println("已重新创建用户数据文件");
+        } catch (Exception e) {
+            System.err.println("备份文件失败: " + e.getMessage());
+        }
+    }
+
+    private void saveUsers() {
+        try {
+            File file = new File(USERS_FILE);
+            file.getParentFile().mkdirs();
+            objectMapper.writerWithDefaultPrettyPrinter().writeValue(file, users.values().toArray(new User[0]));
+        } catch (IOException e) {
+            System.err.println("保存用户数据失败: " + e.getMessage());
+            e.printStackTrace();
+        }
+    }
+
+    public boolean registerUser(String email, String verificationCode) {
+        if (users.containsKey(email)) {
+            return false; // 用户已存在
+        }
+
+        // 生成密码占位符，实际密码在验证后设置
+        String tempPasswordHash = BCrypt.withDefaults().hashToString(12, "temp".toCharArray());
+        User user = new User(email, tempPasswordHash, verificationCode);
+        users.put(email, user);
+        verificationCodeTimestamps.put(email, LocalDateTime.now());
+        saveUsers();
+        return true;
+    }
+
+    public boolean verifyUser(String username, String email, String verificationCode, String password) {
+        User user = users.get(email);
+        if (user == null || !user.getVerificationCode().equals(verificationCode)) {
+            return false;
+        }
+
+        // 检查验证码是否过期
+        LocalDateTime codeTime = verificationCodeTimestamps.get(email);
+        if (codeTime == null || codeTime.plusMinutes(VERIFICATION_CODE_EXPIRY_MINUTES).isBefore(LocalDateTime.now())) {
+            return false;
+        }
+
+        // 验证密码格式
+        if (!validatePassword(password)) {
+            return false;
+        }
+
+        // 设置实际密码
+        String passwordHash = BCrypt.withDefaults().hashToString(12, password.toCharArray());
+        user.setPasswordHash(passwordHash);
+        user.setUsername(username);
+        user.setVerified(true);
+        verificationCodeTimestamps.remove(email);
+        saveUsers();
+        return true;
+    }
+
+    public boolean login(String email, String password) {
+        User user = users.get(email);
+        if (user == null || !user.isVerified()) {
+            return false;
+        }
+
+        BCrypt.Result result = BCrypt.verifyer().verify(password.toCharArray(), user.getPasswordHash());
+        return result.verified;
+    }
+
+    public boolean changePassword(String email, String oldPassword, String newPassword) {
+        User user = users.get(email);
+        if (user == null) {
+            return false;
+        }
+
+        // 验证旧密码
+        BCrypt.Result result = BCrypt.verifyer().verify(oldPassword.toCharArray(), user.getPasswordHash());
+        if (!result.verified) {
+            return false;
+        }
+
+        // 验证新密码格式
+        if (!validatePassword(newPassword)) {
+            return false;
+        }
+
+        // 更新密码
+        String newPasswordHash = BCrypt.withDefaults().hashToString(12, newPassword.toCharArray());
+        user.setPasswordHash(newPasswordHash);
+        saveUsers();
+        return true;
+    }
+
+    public boolean validatePassword(String password) {
+        if (password.length() < 6 || password.length() > 10) {
+            return false;
+        }
+
+        boolean hasUpper = false;
+        boolean hasLower = false;
+        boolean hasDigit = false;
+
+        for (char c : password.toCharArray()) {
+            if (Character.isUpperCase(c)) hasUpper = true;
+            if (Character.isLowerCase(c)) hasLower = true;
+            if (Character.isDigit(c)) hasDigit = true;
+        }
+
+        return hasUpper && hasLower && hasDigit;
+    }
+
+    public boolean userExists(String email) {
+        return users.containsKey(email);
+    }
+
+    public boolean isValidEmail(String email) {
+        return email.matches("^[A-Za-z0-9+_.-]+@(.+)$");
+    }
+}
\ No newline at end of file
diff --git a/src/main/java/mathlearning/ui/LoginFrame.java b/src/main/java/mathlearning/ui/LoginFrame.java
new file mode 100644
index 0000000..a9579d0
--- /dev/null
+++ b/src/main/java/mathlearning/ui/LoginFrame.java
@@ -0,0 +1,111 @@
+package mathlearning.ui;
+
+import mathlearning.model.User;
+import mathlearning.service.UserService;
+
+import javax.swing.*;
+import java.awt.*;
+import java.awt.event.ActionEvent;
+import java.awt.event.ActionListener;
+
+public class LoginFrame extends JFrame{
+    private UserService userService;
+    private JTextField emailField;
+    private JPasswordField passwordField;
+
+    public LoginFrame(UserService userService) {
+        this.userService = userService;
+        initializeUI();
+    }
+
+    private void initializeUI() {
+        setTitle("数学学习软件 - 登录");
+        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
+        setSize(400, 300);
+        setLocationRelativeTo(null);
+        setResizable(false);
+
+        // 主面板
+        JPanel mainPanel = new JPanel(new BorderLayout(10, 10));
+        mainPanel.setBorder(BorderFactory.createEmptyBorder(20, 20, 20, 20));
+
+        // 标题
+        JLabel titleLabel = new JLabel("用户登录", JLabel.CENTER);
+        titleLabel.setFont(new Font("微软雅黑", Font.BOLD, 24));
+        mainPanel.add(titleLabel, BorderLayout.NORTH);
+
+        // 表单面板
+        JPanel formPanel = new JPanel(new GridLayout(3, 2, 10, 10));
+
+        JLabel emailLabel = new JLabel("邮箱:");
+        emailLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        emailField = new JTextField();
+
+        JLabel passwordLabel = new JLabel("密码:");
+        passwordLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        passwordField = new JPasswordField();
+
+        formPanel.add(emailLabel);
+        formPanel.add(emailField);
+        formPanel.add(passwordLabel);
+        formPanel.add(passwordField);
+
+        mainPanel.add(formPanel, BorderLayout.CENTER);
+
+        // 按钮面板
+        JPanel buttonPanel = new JPanel(new FlowLayout());
+
+        JButton loginButton = new JButton("登录");
+        loginButton.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        loginButton.addActionListener(new LoginButtonListener());
+
+        JButton registerButton = new JButton("注册");
+        registerButton.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        registerButton.addActionListener(e -> openRegisterFrame());
+
+        buttonPanel.add(loginButton);
+        buttonPanel.add(registerButton);
+
+        mainPanel.add(buttonPanel, BorderLayout.SOUTH);
+
+        add(mainPanel);
+    }
+
+    private class LoginButtonListener implements ActionListener {
+        @Override
+        public void actionPerformed(ActionEvent e) {
+            String email = emailField.getText().trim();
+            String password = new String(passwordField.getPassword());
+
+            if (email.isEmpty() || password.isEmpty()) {
+                JOptionPane.showMessageDialog(LoginFrame.this,
+                        "请输入邮箱和密码", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            if (userService.login(email, password)) {
+                JOptionPane.showMessageDialog(LoginFrame.this,
+                        "登录成功!", "成功", JOptionPane.INFORMATION_MESSAGE);
+                // 这里可以打开主界面
+                openMainFrame(email);
+            } else {
+                JOptionPane.showMessageDialog(LoginFrame.this,
+                        "邮箱或密码错误", "登录失败", JOptionPane.ERROR_MESSAGE);
+            }
+        }
+    }
+
+    private void openRegisterFrame() {
+        RegisterFrame registerFrame = new RegisterFrame(userService, this);
+        registerFrame.setVisible(true);
+        this.setVisible(false);
+    }
+
+    private void openMainFrame(String email) {
+
+        // 这里先简单显示一个消息，后续可以扩展为主界面
+        JOptionPane.showMessageDialog(this,
+                "欢迎 " + email + "!\n登录成功，主界面功能待实现。",
+                "登录成功", JOptionPane.INFORMATION_MESSAGE);
+    }
+}
diff --git a/src/main/java/mathlearning/ui/RegisterFrame.java b/src/main/java/mathlearning/ui/RegisterFrame.java
new file mode 100644
index 0000000..ebc97c7
--- /dev/null
+++ b/src/main/java/mathlearning/ui/RegisterFrame.java
@@ -0,0 +1,230 @@
+package mathlearning.ui;
+
+import mathlearning.service.EmailService;
+import mathlearning.service.UserService;
+
+import javax.swing.*;
+import java.awt.*;
+import java.awt.event.ActionEvent;
+import java.awt.event.ActionListener;
+
+public class RegisterFrame extends JFrame{
+    private UserService userService;
+    private EmailService emailService;
+    private LoginFrame loginFrame;
+
+    private JTextField nameField;
+    private JTextField emailField;
+    private JButton sendCodeButton;
+    private JTextField codeField;
+    private JPasswordField passwordField;
+    private JPasswordField confirmPasswordField;
+    private JButton registerButton;
+    private JButton backButton;
+
+    private String verificationCode;
+
+    public RegisterFrame(UserService userService, LoginFrame loginFrame) {
+        this.userService = userService;
+        this.loginFrame = loginFrame;
+
+        // 配置邮箱服务（需要替换为真实的邮箱配置）
+        this.emailService = new EmailService(
+                "smtp.qq.com",
+                "587",
+                "2793415226@qq.com",  // 替换为你的QQ邮箱
+                "rmiomlakglpjddhb",  // 替换为你的授权码
+                true
+        );
+
+        initializeUI();
+    }
+
+    private void initializeUI() {
+        setTitle("数学学习软件 - 注册");
+        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
+        setSize(450, 400);
+        setLocationRelativeTo(null);
+        setResizable(false);
+
+        // 主面板
+        JPanel mainPanel = new JPanel(new BorderLayout(10, 10));
+        mainPanel.setBorder(BorderFactory.createEmptyBorder(20, 20, 20, 20));
+
+        // 标题
+        JLabel titleLabel = new JLabel("用户注册", JLabel.CENTER);
+        titleLabel.setFont(new Font("微软雅黑", Font.BOLD, 24));
+        mainPanel.add(titleLabel, BorderLayout.NORTH);
+
+        // 表单面板
+        JPanel formPanel = new JPanel(new GridLayout(5, 2, 10, 10));
+
+        JLabel nameLabel = new JLabel("用户名:");
+        nameLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        nameField = new JTextField();
+
+        JLabel emailLabel = new JLabel("邮箱:");
+        emailLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        emailField = new JTextField();
+
+        JLabel codeLabel = new JLabel("验证码:");
+        codeLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+
+        JPanel codePanel = new JPanel(new BorderLayout());
+        codeField = new JTextField();
+        sendCodeButton = new JButton("发送验证码");
+        sendCodeButton.addActionListener(new SendCodeListener());
+
+        codePanel.add(codeField, BorderLayout.CENTER);
+        codePanel.add(sendCodeButton, BorderLayout.EAST);
+
+        JLabel passwordLabel = new JLabel("密码:");
+        passwordLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        passwordField = new JPasswordField();
+
+        JLabel confirmPasswordLabel = new JLabel("确认密码:");
+        confirmPasswordLabel.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        confirmPasswordField = new JPasswordField();
+
+        formPanel.add(nameLabel);
+        formPanel.add(nameField);
+        formPanel.add(emailLabel);
+        formPanel.add(emailField);
+        formPanel.add(codeLabel);
+        formPanel.add(codePanel);
+        formPanel.add(passwordLabel);
+        formPanel.add(passwordField);
+        formPanel.add(confirmPasswordLabel);
+        formPanel.add(confirmPasswordField);
+
+        mainPanel.add(formPanel, BorderLayout.CENTER);
+
+        // 按钮面板
+        JPanel buttonPanel = new JPanel(new FlowLayout());
+
+        registerButton = new JButton("注册");
+        registerButton.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        registerButton.addActionListener(new RegisterButtonListener());
+
+        backButton = new JButton("返回登录");
+        backButton.setFont(new Font("微软雅黑", Font.PLAIN, 14));
+        backButton.addActionListener(e -> goBackToLogin());
+
+        buttonPanel.add(registerButton);
+        buttonPanel.add(backButton);
+
+        mainPanel.add(buttonPanel, BorderLayout.SOUTH);
+
+        add(mainPanel);
+    }
+
+    private class SendCodeListener implements ActionListener {
+        @Override
+        public void actionPerformed(ActionEvent e) {
+            String email = emailField.getText().trim();
+
+            if (email.isEmpty()) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "请输入邮箱地址", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            if (!userService.isValidEmail(email)) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "邮箱格式不正确", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            if (userService.userExists(email)) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "该邮箱已注册", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            // 生成6位验证码
+            verificationCode = String.valueOf((int)((Math.random() * 9 + 1) * 100000));
+
+            // 发送验证码邮件
+            boolean sent = emailService.sendVerificationCode(email, verificationCode);
+
+            if (sent) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "验证码已发送到您的邮箱，请查收", "成功", JOptionPane.INFORMATION_MESSAGE);
+
+                // 禁用发送按钮60秒
+                sendCodeButton.setEnabled(false);
+                new Thread(() -> {
+                    try {
+                        for (int i = 60; i > 0; i--) {
+                            final int current = i;
+                            SwingUtilities.invokeLater(() ->
+                                    sendCodeButton.setText(current + "秒后重发"));
+                            Thread.sleep(1000);
+                        }
+                        SwingUtilities.invokeLater(() -> {
+                            sendCodeButton.setText("发送验证码");
+                            sendCodeButton.setEnabled(true);
+                        });
+                    } catch (InterruptedException ex) {
+                        ex.printStackTrace();
+                    }
+                }).start();
+
+            } else {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "验证码发送失败，请检查邮箱地址或网络连接", "错误", JOptionPane.ERROR_MESSAGE);
+            }
+        }
+    }
+
+    private class RegisterButtonListener implements ActionListener {
+        @Override
+        public void actionPerformed(ActionEvent e) {
+            String username = nameField.getText().trim();
+            String email = emailField.getText().trim();
+            String code = codeField.getText().trim();
+            String password = new String(passwordField.getPassword());
+            String confirmPassword = new String(confirmPasswordField.getPassword());
+
+            // 验证输入
+            if (email.isEmpty() || code.isEmpty() || password.isEmpty() || username.isEmpty()) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "请填写所有字段", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            if (!password.equals(confirmPassword)) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "两次输入的密码不一致", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            if (!userService.validatePassword(password)) {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "密码必须为6-10位，且包含大小写字母和数字", "错误", JOptionPane.ERROR_MESSAGE);
+                return;
+            }
+
+            // 先注册用户（临时状态）
+            if (userService.registerUser(email, verificationCode)) {
+                // 验证用户并设置密码
+                if (userService.verifyUser(username, email, code, password)) {
+                    JOptionPane.showMessageDialog(RegisterFrame.this,
+                            "注册成功!", "成功", JOptionPane.INFORMATION_MESSAGE);
+                    goBackToLogin();
+                } else {
+                    JOptionPane.showMessageDialog(RegisterFrame.this,
+                            "验证码错误或已过期", "错误", JOptionPane.ERROR_MESSAGE);
+                }
+            } else {
+                JOptionPane.showMessageDialog(RegisterFrame.this,
+                        "注册失败，用户可能已存在", "错误", JOptionPane.ERROR_MESSAGE);
+            }
+        }
+    }
+
+    private void goBackToLogin() {
+        loginFrame.setVisible(true);
+        this.dispose();
+    }
+}