section, we discuss a few open questions.

Acknowledgment {#acknowledgment .unnumbered}
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I was secretly introduced to the fascinating world of homotopy algebras when I studied quantization of gauge systems with my advisor Simon Lyakhovich in Tomsk State University. I would like to thank Simon for his guidance and greet him with his anniversary. I would like to thank S. Shadrin, J. Stasheff, B. Vallette, A. Voronov and T. Willwacher for useful discussions. I am also thankful to J. Stasheff for his remarks on the first draft of the paper. I would like to thank the anonymous referee for carefully reading my manuscript and for many useful suggestions. A large part of this paper was written when I was an assistant professor at the UC Riverside where I had excellent working conditions and great colleagues. I would like to thank anonymous taxpayers of California for supporting the UC system and my work at UC Riverside. The results of this paper were presented at the Southern California Algebra Conference in UCLA and at the Geometry and Physics seminar at Northwestern University. I would like to thank participants of the conference and the seminar for questions and useful comments. I am partially supported 