TITLE: Equilibria in Three Body Problems: stability, invariant tori and connections (Ph.D. Thesis, Advisor: Regina Mart\'{\i}nez) AUTHOR: Anna Sam\`a Departament de Matem\`atiques, Universitat Aut\`onoma de Barelona ABSTRACT In this work we distinguish mainly three parts. In the first one we study some questions related to the stability of homographic solutions. The second part is devoted to the Spatial RTBP. For that problem we study the existence of heteroclinic/homoclinic connections to the invariant tori contained in the centre manifold of the Spatial RTBP. Finally we study the applicability of KAM theorem to the centre manifold of the collinear equilibrium points in the Planar Three Body Problem.