"게" is short for "것이"^^' (This short form is preferred in spoken.) 공부하는 게 ☞ 공부하는 것이(as a subject) 공부한 것은 means "something you studied" (as a topic) like Mojave said above.^^' @Mojave, you're totally right. :) \^o^/

Thanks Mojave! Too many 것 in Korean @.@''... Hahaha...

게 is the contracted form of 것이. And 것이 and 것은 mean "thing" but with different subject particles. 공부하는 is the present form of "to study" as an adjective. 공부한 is the past form of "to study" as an adjective. 공부하는 게 = the thing that I study (with the identifier particle) 공부한 것은 = the thing that I studied (with the topic particle) I hope I got that right.