  This paper presents a thoughful review of: (a) the Clifford algebra Cl(H_{V})
of multivecfors which is naturally associated with a hyperbolic space H_{V};
(b) the study of the properties of the duality product of multivectors and
multiforms; (c) the theory of k multivector and l multiform variables
multivector extensors over V and (d) the use of the above mentioned structures
to present a theory of the parallelism structure on an arbitrary smooth
manifold introducing the concepts of covariant derivarives, deformed covariant
derivatives and relative covariant derivatives of multivector, multiform fields
and extensors fields.
