MyTimer

ButtonPanel.java

package mytimer.gui;

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Font;
import java.awt.event.ActionListener;
import javax.swing.JButton;
import javax.swing.JPanel;

class ButtonPanel extends JPanel {
    private final ActionListener listener;

    ButtonPanel(ActionListener listener) {
        this.listener = listener;

        MyButton start = new MyButton("Start");
        MyButton stop  = new MyButton("Stop");
        MyButton reset = new MyButton("Reset");

        add(start);
        add(stop);
        add(reset);
    }

    class MyButton extends JButton {
        MyButton(String text) {
            this(text, new Dimension(100, 48));
        }
        MyButton(String text, Dimension buttonSize) {
            super(text);
            
            setForeground(Color.BLACK);
            setBackground(Color.WHITE);
            setVerticalAlignment(JButton.CENTER);
            setHorizontalAlignment(JButton.CENTER);
            setActionCommand(text);

            setFont(
                new Font("Arial", Font.PLAIN, 24)
            );
            setPreferredSize(buttonSize);
            
            addActionListener(listener);
        }
    }    
}

GUI.java

package mytimer.gui;

import java.awt.BorderLayout;
import java.awt.event.ActionListener;
import java.awt.event.ActionEvent;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class GUI extends JFrame {
    private ButtonPanel buttonPanel;
    private TimePanel timePanel;

    public GUI(String title) {
        super(title);

        setLayout(new BorderLayout());
        add(
            buttonPanel = new ButtonPanel(new ButtonListener()),
            BorderLayout.CENTER
        );
        add(
            timePanel = new TimePanel(),
            BorderLayout.SOUTH
        );

        pack();
        setLocationRelativeTo(null);
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    }

    class ButtonListener implements ActionListener {
        @Override
        public void actionPerformed(ActionEvent e) {
            switch(e.getActionCommand().toLowerCase()) {
            case "start":
                timePanel.startTimer();
                break;
            case "stop":
                timePanel.stopTimer();
                break;
            case "reset":
                timePanel.resetTimer();
                break;
            default:
                System.out.println(e);
            }
        }
    }
}

MyTimer.java

package mytimer;

import mytimer.gui.GUI;
import javax.swing.SwingUtilities;
import javax.swing.UIManager;

public class MyTimer {
    MyTimer() {
        GUI gui = new GUI("My timer");
        gui.setVisible(true);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            new MyTimer();
        });
    }
}

TimeCount.java

package mytimer.util;

import java.util.Arrays;
import java.util.List;

public class TimeCount {
    private int hour = 0, minute = 0, second = 0;

    public TimeCount countUpSeconds(int secDelta) {
        if(secDelta == 0) return this;

        second += secDelta;
        List<Integer> tmp = TimeCount.divmod(second, 60);
        if(tmp.get(0) == 0) return this;

        second = tmp.get(1);
        return countUpMinutes(tmp.get(0));
    }
    public TimeCount countUpMinutes(int minDelta) {
        if(minDelta == 0) return this;

        minute += minDelta;
        List<Integer> tmp = TimeCount.divmod(minute, 60);
        if(tmp.get(0) == 0) return this;

        minute = tmp.get(1);
        return countUpHours(tmp.get(0));
    }
    public TimeCount countUpHours(int hourDelta) {
        if(hourDelta == 0) return this;

        hour += hourDelta;
        return this;
    }

    // Python-like divmod
    private static List<Integer> divmod(int a, int b) {
        return Arrays.asList(a / b, a % b);
    }

    @Override
    public String toString() {
        return String.format("%02d:%02d.%02d", hour, minute, second);
    }
}

TimePanel.java

package mytimer.gui;

import mytimer.util.TimeCount;
import java.awt.Font;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.Timer;

class TimePanel extends JPanel {
    private Timer timer;
    private TimeCount timeCount = new TimeCount();

    private JLabel timeLabel;

    TimePanel() {
        timeLabel = new JLabel(
            timeCount.toString()
        );
        timeLabel.setFont(
            new Font("Arial", Font.BOLD, 80)
        );
        add(timeLabel);

        timer = new Timer(1000, e -> { 
            timeCount.countUpSeconds(1);
            update();
        });
    }

    void update() {
        timeLabel.setText(timeCount.toString());
        repaint();
    }

    void resetTimer() {
        timeCount = new TimeCount();
        update();
    }
    void startTimer() {
        timer.start();
    }
    void stopTimer() {
        timer.stop();
    }
}