  The main objective of this thesis is a classification project for integral
lattices. Using Kneser's neighbour method we have developed the computer
program tn to classify complete genera of integral lattices. Main results are
detailed classifications of modular lattices in dimensions up to 14 with levels
3,5,7, and 11. We present a fast meta algorithm for the computation of a basis
of a lattice which is given by a large generating system. A theoretical worst
case boundary and practical experiments show important advantages in comparison
to traditional methods. Up to small modifications we use this algorithm for the
decomposition of a lattice into pairwise orthogonal sublattices. As a further
result we prove a covering theorem for the generating system of a lattice. Let
S be a minimal generating system of a lattice of rank n with generators not
larger than B. Then S has at most n + log_2(n!(B/M)^n) elements. We describe
and compute invariants of a lattice L like the spectrum of the discrete Fourier
transform of the length function on L/2L. The numerical computation of a
lattice quantizer and a quantizer of a union of cosets of a lattice are
discussed.
