Last February the first direct detection of gravitational waves has been announced by the LIGO/Virgo collaborations. This discovery marks a milestone for both theoretical and experimental physics, occurring one hundred years after the prediction of gravitational waves by Einstein in 1916, and fifty years after the first experimental efforts to detect them, which started in the 1960s.

This discovery also provides us with a new messenger to probe the universe other than electromagnetic radiation, and opens the era of gravitational wave astronomy. Gravitational waves can be used to collect observational data about the processes underlying the formation and evolution of neutron star and black hole binaries, about the nature of black holes in the centre of galaxies and the formation of structures, and even about the physics of the very early universe. They also provide a very powerful test of General Relativity. The coincident detection of electromagnetic and gravitational radiation from astrophysical objects is expected to bring new information on their nature and can be used to test the evolution of the universe. The future therefore looks very promising for the employment of gravitational waves as a new mean to understand the universe.  

This course is an introduction to the theory of gravitational waves, aiming to provide a basic knowledge of the subject and its principles. It will only present the linearised theory and therefore requires a minimal expertise in General Relativity. Depending on time constraints, the course might end with some applications of gravitational wave physics to cosmology, such as the concept of standard sirens and possible stochastic background of gravitational waves from causal sources operating in the very early universe. 

The plan is the following:

1. Derivation of the wave equation in linearised theory and definition of the transverse traceless gauge
2. Interaction of gravitational waves with test masses and the principles of interferometric detection
3. Definition of the gravitational wave energy momentum tensor and gravitational wave propagation on a curved background
4. Generation of gravitational waves in linearised theory and derivation the quadrupole formula 
5. The inspiral of compact binaries, gravitational wave frequency and waveform
6. Applications to cosmology