  In these Lectures Notes I re-visit the problem of the deep number counts as a
viable method to (1) study the evolution of the galaxy population in the past
and (2) determine the value of the deceleration parameter $q_0$. After a brief
description of the basic concepts needed to model the counts, we show that
simple luminosity evolution models which incorporate dust are able to provide
reasonable fits to both the deep counts and the redshift distribution of faint
field galaxies if $q_0=0.05$. In order to fit the counts in a {\it closed}
($q_0=0.5$) Universe, we include a population of fading dwarfs, more numerous
in the past, based on current ideas to understand the nature of dwarf galaxies.
