Open problems in the theory of finite-dimensional integrable systems and related fields

This paper collects a number of open problems in the theory of integrable systems and related fields, their study being suggested by the main lecturers and participants of the Advanced Course on Geometry and Dynamics of Integrable Systems, from September 9th to 14th 2013, as well as the Conference on Integrability, Topological Obstructions to Integrability and Interplay with Geometry, from September 16th to 20th 2013, both held at the Centre de Recerca Mathematica in Barcelona within the Research Programme “Geometry and Dynamics of Integrable Systems”.