Advanced Algebra, First Edition

Cornerstones, Birkhäuser, Boston, 2007.  ISBN: 0-8176-4522-5.
730+xxiv pages.

Warning:  A second printing of the 2007 first edition appeared in 2015 with many changes.  Externally it is identical to the 2007 version, but internally it is close in content to the digital second edition.  It can be distinguished at once from the 2007 version by a notation of the date on the copyright page.  A discussion of the differences between the digital second edition and the second printing of the first edition may be found here.

A companion volume Basic Algebra was published in its original edition in 2006.
ISBN: 0-8176-3248-4.
ISBN: 0-8176-4533-0 for the two-volume set, Basic Algebra and Advanced Algebra.

There is now a  Digital Second Edition of this book.  It is available only in electronic form.

Chapter Titles:

Transition to Modern Number Theory
Wedderburn-Artin Ring Theory
Brauer Group
Homological Algebra
Three Theorems in Algebraic Number Theory
Reinterpretation with Adeles and Ideles
Infinite Field Extensions
Background for Algebraic Geometry
The Number Theory of Algebraic Curves
Methods of Algebraic Geometry

Files Available:

Corrections:

The final list of corrections to the 2007 version appears in the file below.

Corrections (11/5/2015) - PDF