Childs Lindsay. A concrete introduction to higher algebra

3rd Edition. — New York: Springer, 2009. — xiv, 604 p. — (Undergraduate Texts in Mathematics). — ISBN 978-0-387-74527-5, 978-0-387-74725-5.From a review:This is an introductory level textbook in number theory and higher algebra. I particularly liked the extremely clear language and style of the author. He explains most of the passages first in words and then in formulas, making all steps much less abstract than other algebra books tend to do.I would recommend this especially for self-study, as the book reads exactly as a good teacher talks to a class.Numbers
Numbers
Induction
Euclid’s Algorithm
Unique Factorization
Congruence
Congruence classes and rings
Congruence Classes
Rings and Fields
Matrices and Codes
Congruences and Groups
Fermat’s and Euler’s Theorems
Applications of Euler’s Theorem
Groups
The Chinese Remainder Theorem
Polynomials
Polynomials
Unique Factorization
The Fundamental Theorem of Algebra
Polynomials in Q[x]
Congruences and the Chinese Remainder Theorem
Fast Polynomial Multiplication
Primitive Roots
Cyclic Groups and Cryptography
Carmichael Numbers
Quadratic Reciprocity
Quadratic Applications
Finite Fields
Congruence Classes Modulo a Polynomial
Homomorphisms and Finite Fields
BCH Codes
Factoring Polynomials
Factoring in Z[x]
Irreducible PolynomialsAnswers and Hints to the Exercises

Index