"The author is an important contributor to the subject, and the volume contains many of his results. The book is carefully written … Over 250 exercises, an up-to-date bibliography and an extensive index add to the value of the book. This volume is especially recommended to students and researchers in Algebraic Number Theory, but any algebraist will find here interesting ideas and information."- Studia Universitatis Babes-Bolyai Series Mathematica, Vol. XLVIII, No. 4, 2003"The book is rich in many examples and exercises."-Zentralblatt MATHPromo Copy

• 1: Finite Cogalois Theory; 1: Preliminaries; 2: Kneser Extensions; 3: Cogalois Extensions; 4: Strongly Kneser Extensions; 5: Galois G-Cogalois Extensions; 6: Radical Extensions and Crossed Homomorphisms; 7: Examples of G-Cogalois Extensions; 8: G-Cogalois Extensions and Primitive Elements; 9: Applications to Algebraic Number Fields; 10: Connections with Graded Algebras and Hopf Algebras; 2: Infinite Cogalois Theory; 11: Infinite Kneser Extensions; 12: Infinite G -Cogalois Extensions; 13: Infinite Kummer Theory; 14: Infinite Galois Theory and Pontryagin Duality; 15: Infinite Galois G-Cogalois Extensions