  We describe a method for classifying the Novikov algebras with a given
associated Lie algebra. Subsequently we give the classification of the Novikov
algebras of dimension 3 over R and C, as well as the classification of the
4-dimensional Novikov algebras over C whose associated Lie algebra is
nilpotent. In particular this includes a list of all 4-dimensional commutative
associative algebras over C.
