technically complicated proofs when a suitable reference was available. Namely, we
did not prove Theorem 6.13 about the Kan property of the induced map between
the simplicial Maurer-Cartan spaces. Since operads are not the central topic of this
book, we also omitted proofs of statements from operad theory used in chapters 8
and 9. On the other hand, we explained in detail the relation between the uniform
continuity of algebraic maps and topologized tensor products and included proofs
of the related statements, as this subject does not seem to be commonly known
and the literature is scarce.
This monograph is not the first text attempting to present algebraic deforma-
tion theory. The classical theory is the subject of [GS88], there are lecture notes
[DMZ07] and very recent shorter accounts [Fia08, Gia11]. Useful historical re-
marks can be found in [Pfl06]; an annotated historical bibliography is contained
in [DW], perturbations, deformations, variations and “near misses” are treated in
[Maz04]. There is also the influential though still unfinished book [KS].
Acknowledgments. I would like to express my thanks to the organizers of the
conference, namely to Tom Lada and Kailash Mishra, for the gigantic work they
have done. I am indebted also to the audience, which demonstrated striking tol-
erance to my halting English. During my work on the manuscript, I enjoyed the
stimulating atmosphere of the Universidad de Talca and of the Max-Planck-Institut
f¨ ur Mathematik in Bonn.
In formulating my definition of A∞∞-algebras I profited from conversations
with M. Doubek and M. Livernet. Also, comments and suggestions from T. Gi-
aquinto, A. Lazarev, M. Manetti, J. Stasheff and D. Yau were very helpful. I wish
to thank, in particular, Tom Lada for reading the drafts of the manuscript and
correcting typos and the worst of my language insuﬃciency.