The complement system is a complex system of serum proteins which interact in a cascade, many of the early components are serine proteases which activate each other sequentially. There are two pathways by which complement activation is initiated. The classical pathway is activated by antibody-antigen complexes. The alternative pathway is initiated when a previously activated complement component binds to the surface of a pathogen, where it is protected. Activation of complement has a number of important biological effects.
Nomenclature: the components of the classical pathway are called C1, C2 etc. Where components are proteolytically cleaved, the products are referred to as C2a + C2b etc. Alternative Pathway specific components are given letters as names (factor B etc).
Information provided by: http://www-immuno.path.cam.ac.uk