Quasinormal modes are the modes of a wave propagating in the spacetime around the black hole. The definition is the wave solution that satisfies certain boundary conditions, i.e. only ingoing at the horizon and the outgoing at the infinity. According to these boundary conditions, the corresponding frequencies namely, quasinormal frequencies, are allowed to be a discrete set of complex num- ber. These yield damping modes to the wave solution. Practically, quasinormal frequencies can be numerically obtained by solving the SchrÄodinger-like equation under particular boundary conditions. However, many previous works have sug- gested the possibility to determine these frequencies analytically. Therefore in this thesis, we mainly aim to investigate quasinormal modes of black holes in various dimensions by using analytical method. For three dimensional cases, quasi- normal frequencies of BTZ and rotating BTZ solution are calculated. A large three dimensional AdS Schwarzschild black hole are explored and its quasinormal modes are also obtained. Then, a massive scalar perturbation on four dimensional Schwarzschild metric are numerically investigated. For five dimensions, first order perturbation is applied for the study of quasinormal modes of a five dimensional AdS Schwarzschild background. Ultimately, we have proposed semi-analytic calculation for the quasinormal frequencies of a rotating Kaluza-Klein black hole with squashed horizons.
