  An outline is presented of the Extended Scale Relativity (ESR) in C-spaces
(Clifford manifolds), where the speed of light and the minimum Planck scale are
the two universal invariants. This represents in a sense an extension of the
theory developed by L. Nottale long ago. It is shown how all the dimensions of
a C-space can be treated on equal footing by implementing the holographic
principle associated with a nested family of p-loops of various
dimensionalities. This is achieved by using poly-vector valued coordinates in
C-spaces that encode in one stroke points, lines, areas, volumes,... In
addition, we review the derivation of the minimal-length string uncertainty
relations; the logarithmic corrections (valid in any dimension) to the black
hole area-entropy relation. We also show how the higher derivative gravity with
torsion and the recent results of kappa-deformed Poincare theories of gravity
follow naturally from the geometry of C-spaces. In conclusion some comments are
made on the cosmological implications of this theory with respect to the
cosmological constant problem, the two modes of time, the expansion of the
universe, number four as the average dimension of our world and a variable fine
structure constant.
