  We describe algorithmic methods for the Gauss-Manin connection of an isolated
hypersurface singularity based on the microlocal structure of the Brieskorn
lattice. They lead to algorithms for computing invariants like the monodromy,
the spectrum, and the spectral pairs. These algorithms use a normal form
algorithm for the Brieskorn lattice, standard basis methods for localized
polynomial rings, and univariate factorization. We give a detailed description
of the algorithm to compute the monodromy.
