Preface to the Fourth Edition, 1The Integers, 2 Rational Numbers and Fields, 3: Polynomials, 4: Real Numbers, 5: Complex Numbers, 6: Groups, 7: Vectors and Vector Spaces, 8: The Algebra of Matrices, 9: Linear Groups, 10: Determinants and Canonical Forms, 11: Boolean Algebras and Lattices, 12: Transfinite Arithmetic, 13: Rings and Ideals, 14: Algebraic Number Fields, 15: Galois Theory, Bibliography, List of Special Symbols, Index

Birkhoff , Garrett; Mac Lane , Saunders

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.