  Some years ago we proposed a new approach for the analysis of galaxy and
cluster correlations based on the concepts and methods of modern statistical
physics. This led to the surprising result that galaxy correlations are fractal
and not homogeneous up to the limits of the available catalogues. In the
meantime many more redshifts have been measured and we have extended our
methods also to the analysis of number counts and angular catalogues. This has
led to a complete analysis of all the available data that we are going to
present in detail in this lecture. In particular we will discuss the properties
of the following catalogues: CfA, Perseus-Pisces, SSRS, IRAS, LEDA, Las
Campanas and ESP for galaxies and Abell and ACO for clusters. The usual
statistical methods, that are based on the assumption of homogeneity, are
therefore inconsistent for all the length scales probed until now. A new, more
general, conceptual framework is necessary to identify the real physical
properties of these structures. In the range of self-similarity theories should
shift from "amplitudes" to "exponents". The new analysis shows that all the
available data are consistent with each other and show fractal correlations
(with dimension $D \simeq 2$) up to the deepest scales probed until now ($1000
h^{-1}Mpc$) and even more as indicated from the new interpretation of the
number counts. The distribution of luminous matter in the universe is therefore
fractal and not homogeneous. The evidence for this being very strong up to $150
h^{-1}Mpc$ due to the statistical roboustness of the data and progressively
weaker (statistically) at larger distances due to the limited data. These facts
lead to fascinating conceptual implications about our knowledge of the universe
and to a new scenario for the theoretical challenge in this field.
