  In this survey, we first present basic facts on A-infinity algebras and
modules including their use in describing triangulated categories. Then we
describe the Quillen model approach to A-infinity structures following K.
Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a
conceptual construction of A-infinity functor categories using a suitable
closed monoidal category of cocategories. In particular, this yields a natural
construction of the bialgebra structure on the bar construction of the
Hochschild complex of an associative algebra.
