Clustering in the Universe: from Highly Nonlinear Structures to Homogeneity

These lecture notes concentrate on a few specific topics concerning the distribution of galaxies on scales from 0.1 to nearly 1000/h Mpc. The main aim is to provide the students with the information and tools to familiarize with a few basic questions: 1) What are the scaling laws followed by the clustering of luminous objects over almost four decades of scales; 2) How galaxy motions distort the observed maps in redshift space, and how we can correct and use them to our benefit; 3) Is the observed clustering of galaxies suggestive of a fractal Universe; and consequently, 4) Is our faith in the Cosmological Principle still well placed, i.e. do we see evidence for a homogeneous distribution of matter on the largest explorable scales, in terms of the correlation function and power spectrum of the distribution of luminous objects. For some of these questions we have a well--defined answer, but for some others the goal is to indicate the path along which there is still a good deal of exciting work to be done.