What gravitational signals say about the structure and the evolution of astrophysical sources

Gravitational waves transport very detailed information on the structure and evolution of astrophysical sources. For instance a binary system in the early stages of its evolution emits a wavetrain at specific frequencies that depend on the characteristics of the obital motion; as the orbit shrinks and circularize, due to radiation reaction effects, the orbiting bodies get closer and tidally interact. This interaction may result in the excitation of the proper modes of oscillation of the stars, and in the emission of gravitational signals that carry information on the mode frequencies, and consequently on the equation of state in the stellar interior. These phenomena may occur either in solar type stars with orbiting planets and in compact binaries, and in this lecture we will discuss different approaches that can be used to study these processes in the framework of General Relativity.