Black holes play a fundamental role in modern physics. These possess characteristic resonant frequencies, called Quasinormal Modes (QNMs), which are important in our understanding of the dynamics of astrophysical black holes. Quasinormal modes are single frequency modes dominating the time evolution of perturbations of systems which are subject to damping, either by internal dissipation or by radiating away energy. Due to the damping, the frequency of a quasinormal mode must be complex, its imaginary part being inversely proportional to the typical damping time. In general relativity, damping occurs even without friction, since energy may be radiated away towards infinity by gravitational waves. 

In this thesis, the quasinormal modes for gravitational and electromagnetic perturbations are calculated in a Scalar-Tensor-Vector (STVG) Modified Gravity (MOG) spacetime. This theory is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter.
It is found that for the increasing model parameter a, both the real and imaginary parts of the QNMs decrease compared to those for a Schwarzschild black hole. On the other hand, when taking into account the 1=(1+a) mass re-scaling factor present in MOG, Im(w) matches almost identically that of GR, while Re(w) is higher. These results can be identified in the ringdown phase of massive compact object mergers, and are thus timely in light of the recent gravitational wave detections by LIGO.