Computation of Eigenvalues, Spectral Zeta Functions and   Zeta-Determinants on Hyperbolic Surfaces
  These are lecture notes from a series of three lectures given at the summer school "Geometric and Computational Spectral Theory" in Montreal in June 2015. The aim of the lecture was to explain the mathematical theory behind computations of eigenvalues and spectral determinants in geometrically non-trivial contexts. 
Alexander Strohmaier
math.NA math.SP