  The lecture notes describe the Delaunay Tessellation Field Estimator for
Cosmic Web analysis. The high sensitivity of Voronoi/Delaunay tessellations to
the local point distribution is used to obtain estimates of density and related
quantities. The adaptive and minimum triangulation properties of Delaunay
tessellations are utilized for interpolation to continuous volume-covering
density and velocity fields. The adaptivity to the local density and geometry
preserves three key characteristics of the cosmic matter distribution: 1) its
hierarchical nature,2) its anisotropic weblike morphology, 3) the presence and
structure of voids. The lecture notes discuss the mathematical context and
background of the DTFE method, in essence a first order version of Natural
Neighbour methods, smooth and higher order spatial interpolation techniques.
This is followed by an outline of the DTFE procedure. A series of tests on
spatially complex point distributions provides quantitative information on its
performance and noise characteristics. We conclude with a few cosmological
applications. The reconstruction of the spatial weblike patterns in N-body
simulations and in the 2dFGRS provide a visual impression of DTFE's
performance. The analysis of the velocity divergence pdf and maps obtained of
the velocity flow in the Local Universe (implied by PSCz) illustrate its
promise for probing the dynamics of cosmic structure. The Watershed Void Finder
(Platen et al. 2007), for the study of voids, and Multiscale Morphology Filter
(Aragon-Calvo et al. 2007), for identifying and analyzing weblike networks of
filaments, sheets and clusters, are based upon DTFE density fields. We also
mention SimpleX, a related random lattice radiative transfer formalism
(Ritzerveld & Icke 2006).
