  Observations reveal that on large scales the universe is spanned by a
percolating network of superclusters interspersed with large and almost empty
regions -- voids. This thesis reports the construction of a sophisticated
computational algorithm called SURFGEN which is used to determine the
morphological and topological properties of the cosmic web. SURFGEN generates a
triangulated surface from a discrete data set representing (say) the
distribution of galaxies in real (or redshift) space. SURFGEN then determines,
for this surface, the Minkowski functionals which provide us with an excellent
diagnostic of three dimensional shapes of clusters, superclusters and voids.
SURFGEN is applied to N-body simulations, mock galaxy catalogues as well as to
galaxies in the Las Campanas Redshift Survey. In all cases the morphology of
individual superclusters and voids is determined and the connectedness of the
cosmic web is assessed by means of the Genus curve and percolation analysis. We
demonstrate that SURFGEN can successfully discriminate between rival models of
structure formation and is a very useful tool with which to quantify the
geometrical and topological properties of large scale structure.
