Algebraic Number Theory (Grundlehren Der Mathematischen Wissenschaften)

Rating:
Summary: 10 stars if I could.
Review: After having no fun with Lang's text "Algebraic Number Theory" I began seking out something more complete and which was full of quality exposition. As a result of Amazon's approach to marketing towards members, I was recommended this book and decided quickly that I must have it. This book is marvelously well written, examples are kept to an un-overwhelming minimum, the problems are not trivial (at least to me) and in fact I feel this is the kind of book on par with, say, Paulo Ribenboim's "Classical Theory of Algebraic Numbers" since these are both the type of book you would want to take with you on a long trip or as Paulo says, "while stranded on a desert island". This book is by no means intended for those who are not fluent in both Number Theory as well as Algebra, both at the graduate level and obviously for those who are Mahematically gifted. I highly recommend this book to graduate students interested in Algebraic number theory as well as those needing a splendid reference.

Rating:
Summary: 10 stars if I could.
Review: After having no fun with Lang's text "Algebraic Number Theory" I began seking out something more complete and which was full of quality exposition. As a result of Amazon's approach to marketing towards members, I was recommended this book and decided quickly that I must have it. This book is marvelously well written, examples are kept to an un-overwhelming minimum, the problems are not trivial (at least to me) and in fact I feel this is the kind of book on par with, say, Paulo Ribenboim's "Classical Theory of Algebraic Numbers" since these are both the type of book you would want to take with you on a long trip or as Paulo says, "while stranded on a desert island". This book is by no means intended for those who are not fluent in both Number Theory as well as Algebra, both at the graduate level and obviously for those who are Mahematically gifted. I highly recommend this book to graduate students interested in Algebraic number theory as well as those needing a splendid reference.

Rating:
Summary: Algebraic Number Theory by Neukirch
Review: It there a more beautifully written introduction to contemporary algebraic number theory than Neukirch's Algebraic Number Theory? It is the only introductory text to contain an elementary and accessible account of Arakelov theory in arithmetic geometry, which is the theory of metrized invertible modules of an order of the ring of integers of a number field. The text presupposes familiarity with undergraduate level number theory, complex analysis, and Galois theory.