ABSTRACT
This chapter discusses the notion of normal subgroupoids and quotient groupoids, notions that play an instrumental role in the theory of groups as the keys to understanding their structure. It introduces the notion of simple groupoids and analyses some of its consequences. The chapter discusses the general structure theorem that shows that a connected groupoid is an extension of a groupoid of pairs by its totally disconnect fundamental groupoid. A theorem of classification of groupoids up to order 20 is stated and along its proof, and notions from the general structure of groupoids are applied and extended by developing a simple cohomology theory.
