In this Master's thesis we are concerned with the theory of (pure) motives, which is conjectured to serve as a universal or absolute cohomology theory in algebraic geometry. We begin with a reminder of the classical (Weil) cohomology theories for smooth projective varieties and give hints as to why we should believe that a theory of motives exists. In Chapter $2$, we recall some basic homological algebra, in particular we introduce the notions of additive, pseudo-abelian and abelian categories. We then discuss the theory of Tannakian categories in Chapters $3$ and $4$, where in Chapter 4 we consider the Tannakian theory from the viewpoint of stacks. In Chapter 5 we define the category of pure motives using the theory of algebraic cycles and prove Jannsen's theorem on the semi-simplicity of the category of numerical (pure) motives.
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