Variations of Infinite Derivative Modified Gravity

We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R)F(\mathrm{\square })Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.