That’s my first post here. I’m 18 years old and I’m about to go to college in more or less six months (majoring in Pure Mathematics). I have completed my senior year on December, 2017 and will have until August, 2018 to relax and study by myself. For this reason, I’m looking for some first-year undergrad books about Euclidean and Non-Euclidean Geometry; books that are very didactic - even because I'm going to read and study it by myself.
Just to clarify - and perhaps help you understanding “how much I can handle” -, I’m already studying Abstract Algebra. I am using the “Abstract Algebra: An Introduction” by Thomas W. Hungerford, and I’m handling it, though sometimes it’s hard for me to do some exercises, due to the fact that this is my first contact with proofs. So, I’m looking for some Geometry books that have an “undergrad approach” but are very didactic - i.e, books by mathematicians who break the Theorems and Corollaries into several steps -, just as Thomas Hungerford’s book with Abstract Algebra.
Furthermore, I’m also here to receive suggestions. So, besides giving me your books recommendations, I would like to hear from you if you think it’s a good idea to study both Non-Euclidean and Euclidean Geometry simultaneously.
Thanks in advance to all who will contribute to this discussion, Guilherme.