Introduction to Algebraic K-Theory - Categories and Topology

This book gives a basic introduction to the algebraic K-theory space K(R) without assuming much knowledge in category theory or homotopy theory. The work is divided into two parts. Part I introduces all the necessary tools from category theory and simplicial homotopy theory which one needs to define the K-theory space. Part II defines K(R) and studies the basic properties of these spaces. While many textbooks cover the classical material in algebraic K-theory, this book offers an accessible introduction to this active area of research for graduate students. One can also view these lecture notes as an introduction to the use of categories in homotopy theory, or rather the interaction between the two areas of mathematics.