This thesis is made up of six main chapters and some different appendices. Let us see briefly their most important results: In the chapter called introduction, the metodology which is going to be used is described, as well as the principal objectives we want to achieve in this thesis. In chapter 2 we introduce some important concepts which are needed to understand this thesis. Thus, the Classical Mechanics is described; besides, it comes from the restricted Relativity Theory. First of all, the Lagrangian and Hamiltonian notation is introduced and so the Dynamical systems. Secondly, the Langrange and Hamiltonian equations are given. Thirdly, the canonical transformations and their characteristical functions are studied too. Later, the Hamilton-Jacobi equations are given and also the Liouville and Liouville-Arnold theorems. Then the Lie groups, the Lie algebras and the Lie actions are presented. As they are quite important for us, the simplectic and Poisson manifolds are studied too, as well as the momentum maps and some reduction theorems, which will allow us to reduce significantly the problems we will study during this work.
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