2021-02-072021-02-072009-11-010377-90171573-0530http://dx.doi.org/10.34944/dspace/6049524XD (isidoc)http://hdl.handle.net/20.500.12613/6067We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal. © 2009 The Author(s).103-136enhttps://creativecommons.org/licenses/by-nc/2.0Hochschild complexesdeformation quantizationArticle2021-02-07