This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov

Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vec

Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This t

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory

From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendiec