  We show that the unification of electromagnetism and gravity into a single
geometrical entity can be beautifully accomplished in a theory with
non-symmetric affine connection
(${\Gamma}_{\mu\nu}^{\lambda}\neq{\Gamma}_{\nu\mu}^{\lambda}$), and the
unifying symmetry being projective symmetry. In addition, we show that in a
purely-affine theory where there are no constrains on the symmetry of
${\Gamma}_{\mu\nu}^{\lambda}$, the electromagnetic field can be interpreted as
the field that preserves projective-invariance. The matter Lagrangian breaks
the projective-invariance, generating classical relativistic gravity and
quantum electromagnetism. We notice that, if we associate the electromagnetic
field tensor with the second Ricci tensor and ${\Gamma}_{[\mu\nu]}^{\nu}$ with
the vector potential, then the classical Einstein-Maxwell equation can be
obtained. In addition, we explain the geometrical interpretation of projective
transformations. Finally, we discuss the importance of the role of
projective-invariance in f(R) gravity theories.
