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General Relativity predicts its own demise in the existence of singular black hole solutions. There have been mounting astrophysical evidence that black holes do exist in nature. Thus they are not just pathologies of the theory but fundamental objects in gravity that require understanding. Theoretically, they serve as "laboratories" for studies in quantum gravity; indeed, most of the research in the field aims to resolve various paradoxes and puzzles that emerge when one tries to understand physics inside or outside black holes. The goal of this course is to elucidate these paradoxes and puzzles. First, we will study the classical properties of black holes in general relativity such as horizons, causal history, singularity theorems, area theorems and black hole mining. Next, we will study semi-quantum and quantum properties such as black hole thermodynamics, Hawking radiation, black hole evaporation. We will also explore modern results and perspectives on the fundamental physics of black holes that are necessary for current research. A background in general relativity and quantum field theory is recommended for the course.