• Studying the space of all topological objects of a certain kind
• Space of all finite polyhedra
• Space of all diffeomorphisms of a manifold
• Space of all knots

Higher simple homotopy theory, Annals of Math. 102 (1975), 101–137.

A proof of the Smale conjecture, Annals of Math. 117 (1983), 553–607.

Algebraic Topology, Cambridge University Press, 2002.
(This book is also available online at www.math.cornell.edu/~hatcher.)