The general aim of this book is to provide a modern approach to number
theory through a blending of complementary algebraic and analytic
perspectives, emphasizing harmonic analysis on topological groups. The
more particular goal is to cover John Tate's visionary thesis, giving
virtually all of the necessary analytic details and topological
preliminaries - technical prerequisites that are often foreign to the
typical, more algebraically inclined number theorist. While most of the
existing treatments of Tate's thesis are somewhat terse and less than
complete, the authors' intent is to be more leisurely, more
comprehensive, and more comprehensible. The text addresses students who
have taken a year of graduate-level courses in algebra, analysis, and
topology.