  This is an introductory text on the more topological aspects of contact
geometry, written for the Handbook of Differential Geometry vol. 2. After
discussing (and proving) some of the fundamental results of contact topology
(neighbourhood theorems, isotopy extension theorems, approximation theorems), I
move on to a detailed exposition of the original proof of the Lutz-Martinet
theorem. The text ends with a guide to the literature.
