  MOdified Gravity (MOG) is a covariant modification of Einstein's general
relativity. This theory is one of the current alternatives to dark matter
models. We describe dynamics of collisionless self-gravitating systems in the
context of MOG. By studying the weak field approximation of this theory, we
derive the equations governing the dynamics of the self-gravitating systems.
More specifically, we consider the Jeans instability for self-gravitating fluid
and stellar systems, and derive new Jeans mass limit $\tilde{M}_J$ and
wave-number $\tilde{k}_J$. Furthermore, considering the gravitational
instability in star forming regions, we show that MOG has not a significant
difference with general relativity on this astrophysical scale. However, at
larger scales such as intergalactic space MOG may lead to different galaxy and
structure formation processes.
