I'm a student in university studying math first year. I would like to know what are the best books that shape and build the right math and abstract thinking skills . I don't mind if they are general books. And i prefer an easy read rather than a hard one. Thank you.
I would recommend to start with some mathematical logic and set theory. They could train your rigorous reasoning well enough to deal with any math theory. For logic, First Order Mathematical Logic by Angelo Margaris is an excellent (and cheap!) introductory book to begin with. For set theory, Elements of Set Theory by Herbert B. Enderton is also good enough for introduction (It treats both naive set theory as well as axiomatic way). Later if you are interested in these subjects, there are lots of good books and papers that you can explore.
Personally, I'm not enthusiastic about "learn how to think books". Instead, I believe that one learns how to do by doing. That is, find a topic that interests you and study it and learn it.
When, in the course of doing this, you find you need some background, then learn that background material sufficient so you can move forward in your main topic.
(But, I should add, I'm a physicist and not a mathematician, and maybe this is an important distinction here.)
Spivak's Calculus. Do the exercises, they are great. Especially if you're currently taking calculus (even without proofs).