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The aim of the conference is to bring together specialists in mathematics and mathematical physics to exchange experience and knowledge about the most recent developments in the field of finite dimensional integrable classical and quantum systems. Main topics: o Symplectic and Poisson geometry and integrability o Abelian varieties in algebraic integrable systems o Integrable geodesic flows and natural Hamiltonian systems o Lax representations, separation of variables o Discrete integrable systems, relations to cluster algebras o Applications in mathematical physics, rigid body mechanics, nonholonomic mechanics, and mechatronics o Computer algebra methods in the theory of integrable systems Editions of FDIS have been taking place every other year since 2011 http://fdis2011.uni-jena.de/. Previous editions have taken place in Jena, Luminy http://www.cpt.univ-mrs.fr/fdis13/, and in Bedlewo http://fdis2015.wfa.uz.zgora.pl/. The 2017 edition is the core activity of the Follow-up programme on Geometry and Dynamics of Integrable systems which took place at CRM in September-November 2013.