  In a recent paper, Herrera \cite{2} (L. Herrera: Phys. Rev. D97,
044010(2018)) have proposed a new definition of complexity for static
self-gravitating fluid in General Relativity. In the present article, we
implement this definition of complexity for static self-gravitating fluid to
case of $f(R)$ gravity. Here, we found that in the frame of $f(R)$ gravity the
definition of complexity proposed by Herrera, entirely based on the quantity
known as complexity factor which appears in the orthogonal splitting of the
curvature tensor. It has been observed that fluid spheres possessing homogenous
energy density profile and isotropic pressure are capable to diminish their the
complexity factor. We are interested to see the effects of $f(R)$ term on
complexity factor of the self-gravitating object. The gravitating source with
inhomogeneous energy density and anisotropic pressure have maximum value of
complexity. Further, such fluids may have zero complexity factor if the effects
of inhomogeneity in energy density and anisotropic pressure cancel the effects
of each other in the presence of $f(R)$ dark source term. Also, we have found
some interior exact solutions of modified $f(R)$ field equations satisfying
complexity criterium and some applications of this newly concept to the study
of structure of compact objects are discussed in detail. It is interesting to
note that previous results about the complexity for static self-gravitating
fluid in General Relativity can be recovered from our analysis if $f(R)=R$,
which General Relativistic limit of $f(R)$ gravity. Some future research
directions have been mentioned in the end of the summary.

General Relativity and Quantum Cosmology