This work draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with success to discover theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly...