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This paper is a review of the dynamics of a system of planets. It includesthe study of averaged equations in both non-resonant and resonant systems andshows the great deal of situations in which the angle between the twosemi-major axes oscillates around a constant value. It introduces theHamiltonian equations of the $N$-planet problem and Poincar\'e's reduction ofthem to $3N$ degrees of freedom with a detailed discussion of thenon-osculating ``canonical'' heliocentric Keplerian elements that should beused with Poincar\'e relative canonical variables. It also includes Beaug\'e'sapproximation to expand the disturbing function in the exoplanetary case wheremasses and eccentricities are large. The paper is concluded with a discussionof systems captured into resonance and their evolution to symmetric andasymmetric stationary solutions with apsidal corotation.

Regular motions in extra-solar planetary systems