This tutorial introduces Bayesian networks, a probabilistic graphical model that represents joint probability distributions over a set of variables. Each variable can be discrete or continuous, with states that may be chosen based on modeling needs. Variables are represented by lowercase letters, and sets by uppercase letters. A Bayesian network is a directed acyclic graph where each node represents a variable, and edges represent conditional dependencies. The network encodes conditional independence assertions, allowing the global joint distribution to be constructed from local conditional distributions. The joint probability distribution is determined by the product of local conditional distributions, with each variable depending on its parent nodes. This structure enables efficient computation of probabilities by exploiting conditional independence. However, exact inference in arbitrary Bayesian networks is NP-hard, and approximate methods like Monte Carlo techniques are often used for practical applications. Bayesian networks are constructed using cause-effect relationships, with arcs drawn from causes to their effects. They can be used to model complex interactions, such as the noisy-OR model for multiple causes and a single effect, which reduces computational complexity. Probabilistic inference involves computing the probability of interest using the joint distribution, often through conditional independence to simplify calculations. Various algorithms exist for probabilistic inference, including message-passing schemes, undirected graph transformations, and symbolic simplification. Despite the computational challenges, Bayesian networks are widely used in domains requiring probabilistic reasoning, with ongoing research into efficient inference methods tailored to specific network structures or queries.This tutorial introduces Bayesian networks, a probabilistic graphical model that represents joint probability distributions over a set of variables. Each variable can be discrete or continuous, with states that may be chosen based on modeling needs. Variables are represented by lowercase letters, and sets by uppercase letters. A Bayesian network is a directed acyclic graph where each node represents a variable, and edges represent conditional dependencies. The network encodes conditional independence assertions, allowing the global joint distribution to be constructed from local conditional distributions. The joint probability distribution is determined by the product of local conditional distributions, with each variable depending on its parent nodes. This structure enables efficient computation of probabilities by exploiting conditional independence. However, exact inference in arbitrary Bayesian networks is NP-hard, and approximate methods like Monte Carlo techniques are often used for practical applications. Bayesian networks are constructed using cause-effect relationships, with arcs drawn from causes to their effects. They can be used to model complex interactions, such as the noisy-OR model for multiple causes and a single effect, which reduces computational complexity. Probabilistic inference involves computing the probability of interest using the joint distribution, often through conditional independence to simplify calculations. Various algorithms exist for probabilistic inference, including message-passing schemes, undirected graph transformations, and symbolic simplification. Despite the computational challenges, Bayesian networks are widely used in domains requiring probabilistic reasoning, with ongoing research into efficient inference methods tailored to specific network structures or queries.