Volume 1. Basic concepts ; Introduction : concepts from set theory. The system of natural numbers -- Semi-groups and groups -- Rings, integral domains and fields -- Extensions of rings and fields -- Elementary factorization theory -- Groups with operators -- Modules and ideals -- Lattices.

Volume 2. Linear algebra ; Finite dimensional vector spaces -- Linear transformations -- The theory of a single linear transformation -- Sets of linear transformations -- Bilinear forms -- Euclidean and unitary spaces -- Products of vector spaces -- The ring of linear transformations -- Infinite dimensional vector spaces.

Volume 3. Theory of fields and Galois theory ; Introduction -- Finite dimensional extension fields -- Galois theory of equations -- Abelian extensions -- Structure theory of fields -- Valuation theory -- Artin-Schreier theory.

The three volume Lectures are based on Jacobson's graduate lectures on algebra at Johns Hopkins and Yale in the 1940's and early 1950's, and are very careful, comprehensive and classical in style, giving a general treatment of abstract algebra. The first volume gives a comprehensive introduction to abstract algebra and its basic concepts. The second volume deals with the theory of vector spaces, accompanied by examples and exercises. The third and final volume addresses field theory and Galois theory, and is not an easy read for the casual student, but a serious student who works at the material will be repaid for their efforts. All volumes include a considerable number of exercises are given that vary greatly in difficulty, while the texts in general are example-driven and user-friendly.

Also issued online.