This short (139 pages) work lives up to its name in every sense. The essential elements of algebraic number theory are here, in a format that can be easily read by an advanced undergraduate or beginning graduate student (at whom the book is targeted).
An interesting book like this fills a gap in the textbook market. I recently had a student doing a directed study in algebraic number theory for which this text — an introduction to the essential elements of its subject with clearly stated prerequisites and careful attention to what’s come before — would have been ideal. The book does a nice job of conveying what’s central to algebraic number theory, including some geometry of numbers, cyclotomic fields, and the Riemann hypothesis, while avoiding the temptation to include every tangentially-related topic in the interests of “complete coverage”.
In resisting the quest for an encyclopedic description of algebraic number theory, Chahal has succeeded in writing a book that is “helpful at least to those who do not have the time to plough through voluminous treatises”. Those who have that kind of time will find reading this book to be worth some of their time as well.
Mark Bollman (firstname.lastname@example.org) is an assistant professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted.