Geometry and Quantization of Moduli Spaces [electronic resource] / by Vladimir Fock, Andrey Marshakov, Florent Schaffhauser, Constantin Teleman, Richard Wentworth ; edited by Luis Alvarez Consul, Jørgen Ellegaard Andersen, Ignasi Mundet i Riera.

Loop groups, clusters, dimers and integrable systems -- Lectures on Klein surfaces and their fundamental group -- Five lectures on topological field theory -- Higgs bundles and local systems on Riemann surfaces.

This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.