  We give very precise bounds for the congruence subgroup growth of arithmetic
groups. This allows us to determine the subgroup growth of irreducible lattices
of semisimple Lie groups. In the most general case our results depend on the
Generalized Riemann Hypothesis for number fields but we can state the following
unconditional theorem:
  Let $G$ be a simple Lie group of real rank at least 2, different than
$D_4(\bbc)$, and let $\Gamma$ be any non-uniform lattice of $G$. Let
$s_n(\Gamma)$ denote the number of subgroups of index at most $n$ in $\Gamma$.
Then the limit $\lim\limits_{n\to \infty} \frac{\log s_n(\Gamma)}{(\log n)^2/
\log \log n}$ exists and equals a constant $\gamma(G)$ which depends only on
the Lie type of $G$ and can be easily computed from its root system.
