Seminar course for the Master in Mathematical Physics, Amsterdam University, Fall 2015.

- Physical motivation: deformation quantization, Moyal star product
- The main problem: classification of star products
- Kontsevich formula for the star product
- dg Lie algebras and $L\sub{\infty}$-algebras
- Two dg Lie algebras: the multivector fields and the multidifferential operators
- The Hochschild-Konstant-Rosenberg theorem
- The formality map: graphs and compactification of configuration spaces
- Sketch of proof

- Kontsevich M, Deformation Quantization of Poisson manifolds,
*Lett. Math. Phys.***66**(2003) 157. - Cattaneo A S, Formality and star products. Lecture notes taken by D. Indelicato,
*London Math. Soc. Lecture Note Ser.***323**(2005) 79–144. - Gutt S, Deformation quantisation of Poisson manifolds,
*Geom. Topol. Monogr.***17**(2011) 171-220.