  This paper, the third in a series of eight introduces some of the basic
concepts of the theory of extensors needed for our formulation of the
differential geometry of smooth manifolds . Key notions such as the extension
and generalization operators of a given linear operator (a (1,1)-extensor)
acting on a real vector space V are introduced and studied in details. Also, we
introduce the notion of the determinant of a (1,1)-extensor and the concepts of
standard and metric Hodge (star) operators, disclosing a non trivial and useful
relation between them.
