  This paper introduces an abstract spectral approach to prove effective
equidistribution of expanding horospheres in hyperbolic manifolds. The method,
which is motivated by the approach to counting developed by (Lax-Phillips
1982), produces highly effective, explicit error terms. To exhibit the
flexibility of this method we prove effective horospherical equidistribution
theorems in $T^1(\mathbb{H}^{n+1})$ and in the higher rank setting,
$\operatorname{SL}_n(\mathbb{R})/\operatorname{SO}_n(\mathbb{R})$.
