  In this paper we develop with considerable details a theory of multivector
functions of a $p$-vector variable. The concepts of limit, continuity and
differentiability are rigorously studied. Several important types of
derivatives for these multivector functions are introduced, as e.g., the $A$%
-directional derivative (where $A$ is a $p$-vector) and the generalized
concepts of curl, divergence and gradient. The derivation rules for different
types of products of multivector functions and for compositon of multivector
functions are proved.
