Delve into the intricacies of black hole perturbation theory in this comprehensive lecture, the second installment of a series. Explore advanced concepts and mathematical frameworks used to analyze the behavior of black holes under small disturbances. Gain insights into the latest developments in this field of theoretical physics, including techniques for studying gravitational waves and their interactions with black holes. Examine the applications of perturbation theory in understanding the dynamics of spacetime around these enigmatic cosmic objects. Suitable for graduate students and researchers in physics and astrophysics, this in-depth presentation offers a rigorous exploration of cutting-edge topics in black hole physics.