More than 25% of giant planets are found in multiple systems. Multiplicity is even the rule for low-mass planets. Complex multi-planet systems have been discovered with up to 7 planets orbiting one single star. A fantastic result of the Kepler mission is the high frequency of multi-transiting systems in extremely co-planar packed configurations, probably related to the formation history of these systems. Consistent with the HARPS survey, which revealed that up to 80% of low-mass planets are found in multiple systems, a large number of stars host several transiting planets. Finally, multiple giant planets in the outer regions of systems have now been unveiled as well by direct imaging observations.

Dynamical analysis is therefore a key to understand these systems in terms of stability, orbital inclination, or shaping long-term evolution. Resonant systems and multi-transiting planets are treasure troves in this regard. Resonant configurations provide especially powerful tools for obtaining insight into the formation mechanisms of planetary systems. For example, in such systems planet-planet gravitational interactions can be large enough to induce noticeable variations of the orbital parameters, giving access to the orbital plane inclinations and consequently to the true planetary masses. Transit Timing Variations (TTVs) observed in multiple systems, due to the planet mutual interactions, have enhanced amplitude in resonant systems, making this approach sensitive to additional planets in the system.

Important constraints on planet system architecture are obtained through dynamical analyses of multi-planet systems. Planet interactions during formation and long-term secular/resonant evolution, often also including dissipative processes (disc and tidal effects), shape the system on time scales from a few orbital periods up to the star’s lifetime. A correct treatment of these effects is thus mandatory for a complete understanding of planet formation and evolution, and for a sensible comparison with the actual end-state of the process provided by observation.