Algebra Module Theory written by
William A. Adkins and
Steven H. Weintraub , Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA.
This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adventurous undergraduate might learn some algebra from this book).
Perhaps the principal distinguishing feature of this book is its point of view. Many textbooks tend to be encyclopedic. We have tried to write one that is thematic, with a consistent point of view. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module theory. Having developed it, we present some of its applications: canonical forms for linear transformations, bilinear forms, and group representations.

Algebra Module Theory written by
William A. Adkins, Steven H. Weintraub
cover the following topics.

1. Groups
2. Rings
3. Modules and Vector Spaces
4. Linear Algebra
5. Matrices over PIDs
6. Bilinear and Quadratic Forms
7. Topics in Module Theory
8. Group Representations
Appendix
Bibliography
Index of Notation
Index of Terminology