  We present an adaptation of Voronoi theory for imaginary quadratic number
fields of class number greater than 1. This includes a characterisation of
extreme Hermitian forms which is analogous to the classic characterisation of
extreme quadratic forms as well as a version of Voronoi's famous algorithm
which may be used to enumerate all perfect Hermitian forms for a given
imaginary quadratic number field in dimensions 2 and 3. We also present an
application of the algorithm which allows to determine generators of the
general linear group of an $\O_K$-lattice.
