This volume is based on four advanced courses held at the Centre de Recerca Matem�tica (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.

About the Author

Vladimir V. Fock is Professor at the Institut de Recherche Math�matique Avanc�e in Strasbourg.

Andrey Marshakov is Professor at the National Research University Higher School of Economics in Moscow.

Florent Schaffhauser is Associate Professor at Universidad de Los Andes in Bogot�.

Constantin Teleman is Professor at the University of California in Berkeley.

Richard A. Wentworth is Professor at the University of Maryland.

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