>>12223634These are some of the earliest books I have read. They have definitely shaped my taste and abilities for years to come.
>Herman, Kucera & Simsa, Equations and Inequalities: Elementary problems and theorems in algebra and number theoryIt really helped my computational proficiency. I spent a lot of time working on the exercises in this book in my last year of high school and I can honestly say that I have used everything I learned in there at one point or another.
>Bordellès: Thèmes d'arithmétiqueThis one really sparked my interest for number theory, especially analytic number theory. I did not end up working in that area at all, but it was one of the first books that made me want to pursue math as a career.
>Clark: Elements of abstract algebraThe book that introduced me to algebra. It is interesting in that most of the material is left to the reader as an exercise. The most insightful proofs are given, then most of the other propositions are only stated.
Then, there are of course many more but some of the most important (and pleasant) ones are:
>Atiyah-Macdonald: Introduction to commutative algebra>Borovik: Mirrors and reflections>Caldero & Germoni: Histoires hédonistes de groupes et de géométrie>Milne: Algebraic group schemes>Serre: Complex semisimple Lie algebras>Shafarevich: Basic algebraic geometry 
