We shall assume that the reader possesses a certain familiarity with the rudiments of abstract algebra. More specifically, in addition to the basic properties of integers, sets, and mappings, the reader is expected to know the elementary parts of the theory of groups and the theory of rings, and to possess a reasonable background in linear algebra. Suggested references on these prerequisites are the following.

1. Adamson, I. T. Elementary Rings and Modules. New York: Harper & Row, 1972.

2. Godement, R. Cours d'Algèbre. Paris: Hermann, 1963. (English translation: Algebra. New York: Houghton Mifflin, 1968.)

3. Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.

4. Hoffman, K., and Kunze, R. Linear Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1971.

5. Ledermann, W. Introduction to Group Theory. Edinburgh: Oliver & Boyd, 1973.

6. Rotman, J. J. The Theory of Groups, an Introduction. Boston: Allyn & Bacon, 1973.

This list is not intended as an exhaustive bibliography on the basic concepts of algebra. We have simply selected six easily accessible books that, for our purposes, are particularly suitable as references. The books [1] and [2] seem the most convenient: In the first place, we shall adhere almost completely to the terminology and notation used in these books; furthermore, taken together, these cover all the required background on rings, ideals, polynomials, modules, and vector spaces. The few facts on ordering and cardinal numbers occasionally used here are contained in the book [3]; and each of the books [5] and [6] contains all the background on groups needed in our presentation of Galois theory.