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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Andrew Baker
University of Glasgow
MR ID: 16505
Reference #


Posted date
2020-03-11 13:33:25
Revised date
2022-07-14 17:46:12
Notes type
   Standard Course Offering
      Commutative Algebra
      Group Theory
   Number Theory
      Algebraic Number Theory

An Introduction to Galois Theory

In this course the focus is on the following topics:
• The solution of polynomial equations over a field, including relationships between roots, methods of solutions and location of roots.
• The structure of finite and algebraic extensions of fields and their automorphisms.
We will study these in detail, building up a theory of algebraic extensions of fields and their automorphism groups and applying it to solve problems about roots of polynomial equations.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v2 PDF (824K) 07/15/22