The main difference between this text and others on the same subject, published in the English language, consists in the selection of the material. In proceeding from the elementary to the more advanced properties of equations, the subject of invariants and covariants is here omitted, to make
room for a discussion of the elements of substitutions and substitution-groups, of domains of rationality, and of their application to equations. Thereby the reader acquires some familiarity with the fundamental results on the theory of equations, reached by Gauss, Abel, Galois, and Kronecker.
The Galois theory of equations is usually found by the