This book is a survey of the theory of formal deformation quantization of Poisson manifolds in
the formalism developed by Kontsevich. It is intended as an educational introduction for
mathematical physicists who are dealing with the subject for the first time. The main topics
covered are the theory of Poisson manifolds star products and their classification
deformations of associative algebras and the formality theorem. Readers will also be
familiarized with the relevant physical motivations underlying the purely mathematical
construction.
