I like problem solving. In fact, that is the reason I wanted to study mathematics; This is a field where I could learn the underlying logic of the results rather than just learning ideas even the foremost experts did not necessarily understand.
The issue is that mathematics for the last few semesters have been becoming increasingly abstract, and the distance between what I am learning and actual problem solving seems larger than ever before.
However, I have also read about how the fields I am struggling with are being used in puzzles (a la puzzles Martin Gardner would write about). For instance, Numberphile has three videos on a problem called "Pebbling a Chessboard" in whih the mathematician says that functional analysis is used to prove a result. Also, Euler's solution to the Seven Bridges of Königsberg problem is the first result of topology.
Are there any books through which one can learn topology through problem solving?