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These are lecture notes from a series of three lectures given at the summerschool "Geometric and Computational Spectral Theory" in Montreal in June 2015.The aim of the lecture was to explain the mathematical theory behindcomputations of eigenvalues and spectral determinants in geometricallynon-trivial contexts.

Computation of Eigenvalues, Spectral Zeta Functions and Zeta-Determinants on Hyperbolic Surfaces