  In this work we study a modified version of vacuum $f(R)$ gravity with a
kinetic term which consists of the first derivatives of the Ricci scalar. We
develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and
we emphasize on cosmological applications for a spatially flat cosmological
background. By using the formalism of this theory, we investigate how it is
possible to realize various cosmological scenarios. Also we demonstrate that
this theoretical framework can be treated as a reconstruction method, in the
context of which it is possible to realize various exotic cosmologies for
ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor
counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show
the mathematical equivalence of the two theories.
