We have spent time in high school solving problems in geometry. At that time we didn't care much about whether what we proved actually followed from the axioms. In other words, our proofs may not be correct by modern standards of rigor. There is much more to geometry than just problem solving. It includes the most mind-bending and counter-intuitive ideas I have ever come across in the whole of my academic career. It sure takes time to digest "curved" geometry. I started looking for a book li...