If you want a general overview try finding a book called “Fundamentals of Fame Design” by Ernest Adams. It is a sensible intro, after that - just dive into thematic communities and do your own things.
I know nothing about formal game design education sorry.
Also, because the keys "F" and "G" are adjacent in the keyboard layout, I believe you made a typo in the book title where you wrote Fame instead of Game.
I know nothing about formal game design education sorry.