  This article explores some simple examples of L-infinity algebras and the
construction of miniversal deformations of these structures. Among other
things, it is shown that there are two families of nonequivalent L-infinity
structures on a 1|1 dimensional vector space, two of which are Lie algebra
structures. The main purpose of this work is to provide a simple effective
procedure for constructing miniversal deformations, using the examples to
illustrate the general technique. The same method can be applied directly to
construct versal deformations of Lie algebras.
