The purpose of this chapter is to present the key properties of fuzzy logic and adaptive nets and demonstrate how to use these, separately and in combination, to design intelligent systems. The first section introduces the concept of fuzzy sets and their basic operations. The t and s norms are used to define a variety of possible intersections and unions. The next section shows two ways to estimate membership functions, polling experts, and using data to optimize parameters. Section three shows how any function can be extended to arguments that are fuzzy sets. Section four introduces fuzzy relations, fuzzy reasoning, and shows the first steps to be taken to design an intelligent system. The Mamdami model is defined in this section. Reinforcement-driven agents are discussed in section five. Sections six and seven establish the basic properties of adaptive nets and use these to define the Sugeno model. Finally, the last section discusses neuro-fuzzy systems in general. The solution to the inverted pendulum problem is given by use of fuzzy systems and also by the use of adaptive nets. The ANFIS and CANFIS architectures are defined.