0 Preliminaries.- 1 Vector Spaces.- 2 Linear Transformations.- 3 The Isomorphism Theorems.- 4 Modules I.- 5 Modules II.- 6 Modules over Principal Ideal Domains.- 7 The Structure of a Linear Operator.- 8 Eigenvalues and Eigenvectors.- 9 Real and Complex Inner Product Spaces.- 10 The Spectral Theorem for Normal Operators.- 11 Metric Vector Spaces.- 12 Metric Spaces.- 13 Hilbert Spaces.- 14 Tensor Products.- 15 Affine Geometry.- 16 The Umbral Calculus.- References.- Index of Notation.

This book covers an especially broad range of topics, including some topics not generally found in linear algebra books The first part details the basics of linear algebra. Coverage then proceeds to a discussion of modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators.