Fields and Galois Theory

v2.01 (August 21, 1996). First version on the web.
v2.02 (May 27, 1998). Minor corrections; 57 pages.
v3.0 (April 3, 2002). Revised notes; minor additions to text; added 82 exercises with solutions, an examination, and an index; 100 pages.
v3.01 (August 31, 2003). Minor corrections; numbering unchanged; 99 pages.
v4.00 (February 19, 2005). Minor corrections and improvements; added proofs to the section on infinite Galois theory; added material to the section on transcendental extensions; 107 pages.
v4.10 (January 22, 2008). Minor corrections and improvements; added proofs for Kummer theory; 111 pages.
v4.20 (February 11, 2008). Replaced Maple with PARI; 111 pages.

Contents

1. Basic definitions and results.
2. Splitting fields; multiple roots.
3. The fundamental theorem of Galois theory.
4. Computing Galois groups.
5. Applications of Galois theory.
6. Algebraic closures
7. Infinite Galois theory
8. Transcendental Extensions.

Errata