In this course I will give an overview of different line of sight and environmental effects that are expected to modify/distort a gravitational wave (GW) signal emitted by an astrophysical source at cosmological distance. After an overview of the state of the art of GW observations, I will review the derivation of the waveform emitted by a binary system of compact objects in a flat background, in the newtonian approximation. I will then consider a cosmological context and introduce the concept of standard siren. Finally I will derive which is the expected distortion of an emitted waveform induced by the presence of peculiar velocities and (strong) gravitational lensing.

Lecture 1 — Gravitational waves–introduction
Lecture 2 — Gravitational waves–propagation effects in waveform modeling[-]