This book proposes a new interpretation of the main con- cepts of Theoretical Physics. Using the right instruments of modern Math- ematics, without the introduction of exotic assumptions, it validates the computing methods generally accepted, giving a safer environment to their use, enlarges the scope of crucial theories such as gauge Theory of Fields and General Relativity, and makes possible the exploration of new ideas, notably for gravitation. Following von Neuman seminal work, the foundations of Quantum Me- chanics has been searched in a formal system to express the results of ex- periments. Here another way is explored : the main axioms of QM (Hilbert spaces, observables,...) can be proven, from the common mathematical properties of most models in Physics. The results can then be implemented in a controlled way, at any scale. The Geometry of General Relativity is introduced in the formalism of Fiber bundles and tetrad, which makes easy the deduction and use of the main concepts of the theory, without the cumbersome computations involving the metric. The Kinematics of particles is introduced through the concept of spinors. Using fully the power of Clifford Algebras it is possible to rep- resent the motion (translation and rotation) and the kinematic properties of particles, including their spin, by a single geometric quantity easy to manipulate in the GR context. It gives a firrm ground to the concept of matter Field, of antiparticle, and makes possible the introduction of a clear and operational concept of deformable solid, which can be implemented in Astrophysics. The treatment of gravitation as a Gauge Field, on a footing similar to the other force fields, enlarges the scope of GR, enabling to deal easily with connections other than the Levy-Civita connection, and to use the Riemann tensor, which appears to be more physically significant than the scalar curvature. The rotational and transversal components of the gravitational field are obvious in this formalism, which raises questions about their physical meaning, notably in a Cosmological context. The basic properties of lagrangians are recalled and some useful theorems proven. Two simple, but with a large scope, models implementing the Prin- ciple of Least Action are presented, showing the possibility to make full computations in the formalism introduced in the book. They lead to a good understanding of Noether currents. A last chapter introduces the idea of bosons as discontinuities of the po- tential of gauge fields. The book gives a comprehensive introduction to the mathematical tools which are nowadays mandatory in Theoretical Physics (group representa- tions, fiber bundles, connections, Clifford algebras) and shows how and why they can be implemented in the usual theories.