  The aim of this paper is to start the study of multilinear generalizations of
the classical ideals of linear operators of type $p$ and cotype $q$. As a first
step in a theory we believe will be long and fruitful, we propose a notion of
type and cotype of multilinear operators and the resulting classes of such
mappings are studied in the setting of the theory of Banach/quasi-Banach ideals
of multilinear operators. Distinctions between the linear and the multilinear
theories are pointed out, typical multilinear features of the theory are
emphasized and many illustrative examples are provided. The classes we
introduce are related to the multi-ideals generated by the linear ideals of
operators of some type/cotype and are proved to be maximal and Aron-Berner
stable.
