In this dissertation we study the Laplace operator acting on functions on a smooth,
compact Riemannian manifold. Our approach is based on the study of the spectrum
of the aforementioned operator. The main objects of
our interest are the counting function of the Laplacian and its Riesz means. We discuss the asymptotics of aforementioned functions when the argument approaches infinity.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.