Semi analytical description of formation of galaxies and clusters of
  galaxies
  We apply the well known semi analytical model of formation of DM halos to
discuss the process of formation and evolution of the relaxed objects dominated
by the DM component (such as the first and dSph galaxies and clusters of
galaxies). On the one hand this approach allows us to obtain a simple
description of evolution of the first galaxies. On the other hand it reveals
links between the observed characteristics of the relaxed DM halos and the
initial power spectrum of density perturbations. Results of our analysis of the
observed properties of 41 DM dominated dSph galaxies and data of $\sim 300$
clusters of galaxies are consistent with the $\Lambda$CDM like power spectrum
of initial perturbations down to the scale of $\sim 10kpc$.
