Counting primes, groups and manifolds ====================================== Alex Lubotzky (Jerusalem) Let D be a finitely generated group. Let G be a semisimple Lie group, K a maximal compact subgroup and Y=G/K the associated symmetric space. Let x be a positive real number (going to infinity). We will discuss questions of the following type: How many primes are there which are small than x ? How many subgroups D has, of index at most x? How many quotient manifolds Y has, of volume at most x? We will show that these seemingly unrelated questions are actually connected in several different ways.