John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of three previous Springer books: the first edition (2000) and second edition (2010) of Introduction to Topological Manifolds and Riemannian Manifolds: An Introduction to Curvature (1997).