This paper is an updated version of lectures given at the Helmholtz Summer School on Extrasolar Planetary Systems (Potsdam, 2003). It includes five sections: Orbit determination, the known planetary systems, chaos, transition from secular to resonant dynamics and planetary migration. The first section is mainly devoted to problems arising in the orbit determination of systems with 2 or more planets from data on the radial velocity of the central star. In the second section, an attempt of classification is done in which the known planetary systems are grouped in 4 classes, one of which includes 47 UMa and our Solar System (orbits with low period ratio and small eccentricities). The phenomena related to mean-motion resonances (MMR) are studied with some detail in the remaining sections, since they may directly affect the stability of many systems. In the appendix, the FFT techniques used in the paper to assess the stability of a system are reviewed.