The Large Scale Structure in the galaxy distribution is investigated using Data Release 1 of the Sloan Digital Sky Survey. Using the Minimal Spanning Tree technique we have extracted sets of filaments, of wall-like structures, of galaxy groups, and of rich clusters from this unique sample. The physical properties of these structures were then measured and compared with the statistical expectations based on Zel'dovich theory.The measured characteristics of galaxy walls were found to be consistent with those for a spatially flat ΛCDM cosmological model with Ωm≈ 0.3 and ΩΛ ≈ 0.7, and for Gaussian initial perturbations with a Harrison - Zel'dovich power spectrum. Furthermore, we found that the mass functions of groups and of unrelaxed structure elements generally fit well with the expectations from Zel'dovich theory. We also note that both groups and rich clusters tend to prefer the environments of walls, which tend to be of higher density, rather than the environments of filaments, which tend to be of lower density.