  This paper gives an elementary introduction to noncommutative deformations of
modules. The main results of this deformation theory are due to Laudal.
  Let k be an algebraically closed (commutative) field, let A be an associative
k-algebra, and let M = {M_1, ..., M_p} be a finite family of left A-modules. We
study the simultaneous formal deformations of the family M, described by the
noncommutative deformation functor Def(M): a(p) -> Sets introduced by Laudal.
In particular, we prove that the deformation functor Def(M) has a
pro-representing hull H(M), unique up to non-canonical isomorphism, and
describe how to calculate H(M) using the Ext groups of the family M and their
matric Massey products.
