The implementation problem lies at the heart of a theory of institutions. Simply stated, the aim of implementation theory is to investigate in a rigorous way the relationships between outcomes in a society and how those outcomes arise. The first part of "Bayesian Implementation" presents a basic model of the Bayesian implementation problem and summarizes and explains recent developments in this branch of implementation theory. Substantive problems of interest such as public goods provision, auctions and bargaining are special cases of the model, and these are addressed in subsequent chapters.