Meticulous and complete, this presentation is geared toward upper-level undergraduate and graduate students. A third of the text focuses on the basic ideas of algebraic theory, giving detailed explanations of integral functions, permutations, and groups. A study of the theory of Lagrange follows, using Lagrange's solvent as a basis for the solution of the general quadratic, cubic, and biquadratic equations. After a discussion of various groups (including isomorphic, transitive, and Abelian groups), the text presents a detailed study of Galois theory and concludes with the application of Galoisian theory to the solution of special equations. Many numerical examples with complete solutions appear throughout the book. 1930 ed.