This textbook provides a systematical introduction of Bayesian signal processing from Bayesian parameter estimation, factor graph, and message passing to sparse Bayesian inference (compressive sensing). The book not only provides a systematical introduction of the theory and methods in Bayesian inference, but also discusses advanced Bayesian inference methods recently developed for future wireless systems and its applications in emerging wireless technologies, including massive MIMO, wireless localization, integrated sensing and communications, etc. The authors include a unified framework to incorporate different Bayesian inference methods/algorithms, and a thorough comparison of the pros and cons of different Bayesian inference methods/algorithms and their application scenarios in wireless network and IoT. The authors offer classroom materials such as homework problems, course projects, a solutions manual, PowerPoint slides, and sample code. The book is intended for senior undergraduates, graduate and advanced graduate students and is also suitable for industry researchers.