Free Homotopy Algebras

This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be described and what can be said about the structure of the universal enveloping A(m)-algebra of an L(m)-algebra, and then circulated as a "personal communication." I must honestly admit that it contains no really deep result and that everything I did was that I expanded definitions and formulated a couple of statements with more or less obvious proofs.