The document discusses key concepts in probability theory including random variables, sample spaces, events, atomic events, laws of probability, conditional probabilities, independence, multivariate distributions, and Bayes' theorem. Random variables can be discrete or continuous. A sample space represents all possible outcomes and events are subsets of the sample space. The probability of the sample space is 1 and probabilities of events range from 0 to 1. Conditional probabilities and independence are discussed. Bayes' theorem provides a way to calculate conditional probabilities.