The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic the

The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many othe

A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.