Weak Deflection Angle via Gauss-Bonnet Theorem

Researchers have come a long way in understanding our universe. The chief objective of this piece of text is to augment and improve the contributions to that ever-changing world of mysteries in Physics, in particular, black holes. Various kinds of black holes are discussed along with the potential influencing factors... some conventional facets, some customised. The underlying vision of this research is to provide as many analyses with as few assumptions as possible so that future works, observations, and/or experiments can have a solid set of references. The main focus of this research is studying the gravitational lensing caused by black holes and employing the Gauss-Bonnet theorem to evaluate the weak deflection angle. Five different types of black holes with various kinds of consequences. The advantages, approximations, and disadvantages of every derivation are also mentioned. Several attempts to minimize presumptions were made in this work irrespective of how complicated it is, though, a few still happen to exist, mostly limited by current technology. New discoveries about the cosmos happen every day inching one step closer to the ultimate truth. After all, lesser premises mean more authenticity. Keywords: Black Hole, Gravitational Lensing, Gauss-Bonnet Theorem, Weak Deflection Angle, General Relativity, Quantum Cosmology, Quantum Gravity, Plasma, Dark Matter.