The direct detection of gravitational waves in 2015 has initiated a new era of gravitational wave astronomy, which has already paid remarkable dividends in our understanding of astrophysics and gravitational physics. Aimed at advanced undergraduates and graduate students, this book introduces gravitational waves and its many applications to cosmology, nuclear physics, astrophysics and theoretical physics. The material is presented in a pedagogical way, through Fermi estimates, and detailed explanations and discussions. The student will not only learn what gravitational waves are and how they are produced, but also how they can be used to learn about astrophysical phenomena and cosmological observations, to investigate the interior of neutron stars, and to test general relativity when black holes and neutron stars collide.