This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos's scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.

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List of speakers who confirmed their interest:.- Manuel Asorey (Universidad de Zaragoza, Spain).- A.P. Balachandran (Syracuse University, New York, USA).- Albero Saa (University of Campinas (UNICAMP), Brazil).- José F. Cariñena (Universidad de Zaragoza, Spain).- Fernando Falceto (Universidad de Zaragoza, Spain).- J. Gracia-Bondia (Universidad de Zaragoza, Spain).- José G. Llavona (Universidad Complutense de Madrid, Spain).- Franco Magri (Università degli Studi di Milano-Bicocca, Italy).- Giuseppe Marmo (Università di Napoli Federico II, Italy).- Juan Carlos Marrero (Universidad de La Laguna, Spain).- Juan Manuel Pérez-Pardo (Universidad Carlos III, Spain).- Miguel A. Rodríguez (Universidad Complutense de Madrid, Spain).- Fernando Lledó (Universidad Carlos II de Madrid, Spain).- F. Lizzi (Università di Napoli Federico II, Italy).- Antonio García (Universidad Carlos III de Madrid, Spain).- Narciso Román Roy (Technical University of Catalonia , Spain).- Patricia Vitale (Università di Napoli Federico II, Italy).