Bertrand Berche is author of about 140 research articles in various fields of physics, mainly statistical physics, condensed matter physics, gauge field theories applied to condensed matter systems, field theories in gravitation and cosmology, but also in complex systems and history of sciences. He taught in various countries, France, Mauritania, Venezuela, Ukraine, Cameroon.Ernesto Medina is the author of about 120 research articles, mainly in condensed matter physics, but also in statistical mechanics and granular media, and most recently in gauge field theories applied to spin active low dimensional systems. He was a Fulbright Scholar at Arizona State University and is a Fellow of the American Physical Society.

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• Notation and useful formulas.- Introduction to energy minimization.- Introduction to Lagrangian and Hamiltonian formalisms.- Space-time symmetries, Lie groups, Lie algebras and their representations.- Spacetime symmetries in Minkowski manifold.- Relativistic field theory.- Differential geometry.- Gauge field theory.- A fibre bundle approach to gauge theory.- Curved spacetime field theory.- Alternative relativistic field theories.- Beyond the least action, Path Integral formalism to Quantum Mechanics.