  We consider deformations of finite or infinite dimensional Lie algebras over
a field of characteristic 0. There is substantial confusion in the literature
if one tries to describe all the non-equivalent deformations of a given Lie
algebra. It is known that there is in general no "universal" deformation of the
Lie algebra L with a commutative algebra base A with the property that for any
other deformation of L with base B there exists a unique homomorphism f: A -> B
that induces an equivalent deformation. Thus one is led to seek a "miniversal"
deformation. For a miniversal deformation such a homomorphism exists, but is
unique only at the first level. If we consider deformations with base spec A,
where A is a local algebra, then under some minor restrictions there exists a
miniversal element. In this paper we give a construction of a miniversal
deformation.
