  We study supersymmetric and super Poincar\'e invariant deformations of
ten-dimensional super Yang-Mills theory and of its dimensional reductions. We
describe all infinitesimal super Poincar\'e invariant deformations of equations
of motion of ten-dimensional super Yang-Mills theory and its reduction to a
point; we discuss the extension of them to formal deformations. Our methods are
based on homological algebra, in particular, on the theory of L-infinity and
A-infinity algebras. The exposition of this theory as well as of some basic
facts about Lie algebra homology and Hochschild homology is given in
appendices.
