  In this paper we provide a \emph{global} investigation of the geometry of
parallelizable manifolds (or absolute parallelism geometry) frequently used for
application. We discuss the different linear connections and curvature tensors
from a global point of view. We give an existence and uniqueness theorem for a
remarkable linear connection, called the canonical connection. Different
curvature tensors are expressed in a compact form in terms of the torsion
tensor of the canonical connection only. Using the Bianchi identities, some
interesting identities are derived. An important special fourth order tensor,
which we refer to as Wanas tensor, is globally defined and investigated.
Finally a double-view for the fundamental geometric objects of an absolute
parallelism space is established: The expressions of these geometric objects
are computed in the parallelization basis and are compared with the
corresponding local expressions in the natural basis. Physical aspects of some
geometric objects considered are pointed out.
