Foundations of Galois Theory - (Dover Books on Mathematics) by M M Postnikov (Paperback)

This book provides a comprehensive and self-contained introduction to Galois theory, covering both the basics of the subject and its applications in solving equations by radicals.

Written by a prominent mathematician, it offers advanced undergraduate and graduate students a clear and concise overview of the fundamental concepts and techniques of Galois theory, including the structure of important types of extensions, the field of algebraic numbers, normal extensions, the order and correspondence of the Galois group, and more.

The second part of the book explores the solution of equations by radicals, examining equations solvable by radicals and their construction, before concluding with a detailed analysis of the unsolvability by radicals of the general equation of degree n >= 5.

With its strong historical relevance and concrete applications, this text is an excellent introduction to group theory and provides a solid foundation for further study in abstract algebra.