Explore the foundations of categorical probability theory in this comprehensive 1.5-hour lecture series. Delve into Kleisli categories and their relationship with probability, starting with an introduction to the Giry monad and progressing to the Kleisli category of a monad. Examine Markov kernels and their role in probabilistic modeling. Investigate stochastic maps, focusing on conditional probabilities, their composition, and products. Learn about almost everywhere equivalence and conclude with an in-depth look at Bayes' theorem, providing a solid understanding of the mathematical underpinnings of probabilistic reasoning.