Let $\Gamma$ be a group and $r_n\left(\Gamma \right)$ the number of its $n$-dimensional irreducible complex representations. We define and study the associated representation zeta function ${𝒵}_{\Gamma }\left(s\right)={\sum }_{n=1}^{\infty }{r}_n\left(\Gamma \right)n^{-s}$. When $\Gamma$ is an arithmetic group satisfying the congruence subgroup property then ${𝒵}_{\Gamma }\left(s\right)$ has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place...