TITLE: New families of Solutions in $N$--Body Problems AUTHOR: Carles Sim\'o Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain e-mail: carles@maia.ub.es ABSTRACT: The $N$--body problem is one of the outstanding classical problems in Mechanics and other sciences. In the Newtonian case few results are known for the 3--body problem and they are very rare for more than 3 bodies. Simple solutions, as the so called {\em relative equilibrium solutions}, in which all the bodies rotate around the center of mass keeping the mutual distances constant, are in themselves a major problem. Recently, the first example of a new class of solutions has been discovered by A. Chenciner and R. Montgomery. Three bodies of equal mass move periodically on the plane along the same curve. This work presents a generalization of this result to the case of $N$ bodies. Different curves, to be denoted as {\em simple choreographies}, have been found by a combination of different numerical methods. Some of them are given here, grouped in several families. The proofs of existence of these solutions and the classification turn out to be a delicate problem for the Newtonian potential, but an easier one in strong force potentials.