  In this paper, deformations of $L_\infty$-algebras are defined in such a way
that the bases of deformations are $L_\infty$-algebras, as well. A universal
and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose
cotangent complex admits a splitting. The paper also contains an explicit
construction of a minimal $L_\infty$-structure on the homology $H$ of a
differential graded Lie algebra $L$ and of an $L_\infty$-quasi-isomorphism
between $H$ and $L$.
