Gravitational waves in (2 + 1) dimensions

The gravitational waves, which have been remained undiscovered for a long time, are of great importance since it is thought, they would contribute to the explanation of many secrets of the universe originating from Big Bang. As well as there are studies of many experimental research groups (VIRGO, LISA, etc.), especially the LIGO, many theoretical studies have contributed to the existence of these waves. It is very important to investigate the properties of these waves because these contain crucial information resources of gravitational waves. Besides, the gravitational waves, which are expected to explain dark matter and dark energy, are located in the focus of the various alternative theories. In this thesis, new gravitational wave backgrounds and their interactions with the field of the spin-1/2, spin-1 ve spin-0 particles are investigated in the (2+1) dimensional spacetimes within the framework of the alternative gravitational theories. Within the scope of these theories, the quasinormal frequencies of the gravitational waves are presented.