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In September 2015, one hundred years after Einstein’s prediction of the existence of gravitational waves, the LIGO/Virgo collaboration detected the gravitational radiation produced by the merger of two black holes, marking the beginning of a new era in astronomy. This course will review the theory of gravitational waves, the main astrophysical and cosmological sources of gravitational radiation, and the modeling of these sources through numerical and analytical techniques. We will discuss how present and future gravitational wave detections on Earth and in space can be used to study the astrophysics of compact objects (such as black holes and neutron stars) and to test Einstein’s theory of general relativity.