There have been enormous recent advances in our ability to produce and trap samples of translationally cold molecules (below 1 K) and ultracold molecules (below 1 mK). Molecules such as NH3, OH and NH have been cooled from room temperature to the milliKelvin regime by a variety of methods including buffer-gas cooling and Stark deceleration. Bose-Einstein condensates have been produced for dimers of both bosonic and fermionic alkali metal atoms, and the first signatures of ultracold triatomic and tetraatomic molecules have been observed. This book will include both cooling of molecules from high temperatures and formation of molecules in ultracold atomic gases; molecules in cold ionic gases and in helium droplets will also be covered. .