In this chapter we introduce the definitions of the SEMIFLOW associated to a dissipative autonomous dynamical system in a Banach space, and of the attractor of this semiflow. We discuss some of the most relevant properties of semiflows and their attractors. As we shall see, the ideas and results presented in this chapter are a natural generalization to the infinite dimensional case of many well known notions of the qualitative theory of ODEs (where the dimension of the space is finite). Throughout this chapter, X is a Banach space, with norm ‖ · ‖ and induced distance d; however, most of the results we establish also hold in general complete metric spaces.