Some books I enjoyed as a first year undergraduate:

Abstract Algebra by Dummit and Foote: I have heard many people speak ill of this text. However, from the perspective of one who is interested in picking up the fundementals of algebra, in my opinion this is the text.

Introduction to Topological Manifolds by Lee: Don't let the word manifold scare you off. This book is essentially an introductory topology book with all of the boring bits left out. I know it is a GTM but I was able to pick it up during my first year of Uni and learn a lot of topology from it.

Munkres topology: This is "the" book for learning point set topology. It is a bit gentler than Lee's and goes through all the relevant set theory you will ever need (unless you become a set theorist). I picked this book up during my first year at Uni and have been opening it regularly ever since.