Just right click anywhere on the game screen, click ''Settings'' and then right click again with the settings still open, and click ''Play''. In adventure mode, this will work until level 4, but ones you completed level 4, it will be able to skip levels again.
In Classic, Adventure, or All-Star mode, right click at the top left. If done correctly, a bar will appear. Click on forward (on the bar) to skip to the next level. In Training mode, do the same thing and it will advance you to the next level.
In Training mode, the last level you go to will be the credits. You cannot play at the credits.
After the credits you will be taken to the main menu.