  To investigate the origin and nature of inertia, we introduce a new concept
of hypothetical 2D, so-called, "master-space" (MS), subject to certain rules.
The MS, embedded in the background 4D-spacetime, is an indispensable individual
companion to the particle of interest, without relation to every other
particle. We argue that a deformation/(distortion of local internal properties)
of MS is the origin of inertia. With this perspective in sight, we construct
the alternative relativistic theory of inertia (RTI), which allows to compute
the relativistic inertial force acting on an arbitrary point-like observer due
to its "absolute acceleration". We go beyond the hypothesis of locality with an
emphasis on distortion of MS, which allows to improve essentially the standard
metric and other relevant geometrical structures related to the noninertial
reference frame of an arbitrary accelerated observer. We compute the inertial
force exerted on the photon in a gravitating system in the semi-Riemann space.
Despite the totally different and independent physical sources of gravitation
and inertia, this approach furnishes justification for the introduction of the
principle of equivalence. Consequently, we relate the inertia effects to the
more general post-Riemannian geometry. We derive a general expression of the
relativistic inertial force exerted on the extended spinning body moving in the
Rieman-Cartan space.
