  In this article, we provide a pedagogical review of the
Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe
static, spherically symmetric gaseous stars in general relativity. Our
discussion starts with a systematic derivation of the TOV equation from the
Einstein field equations and the relativistic Euler equations. Next, we give a
proof for the existence and uniqueness of solutions of the TOV equation
describing a star of finite radius, assuming suitable conditions on the
equation of state characterizing the gas. We also prove that the compactness of
the gas contained inside a sphere centered at the origin satisfies the
well-known Buchdahl bound, independent of the radius of the sphere. Further, we
derive the equation of state for an ideal, classical monoatomic relativistic
gas from statistical mechanics considerations and show that it satisfies our
assumptions for the existence of a unique solution describing a finite radius
star. Although none of the results discussed in this article are new, they are
usually scattered in different articles and books in the literature; hence it
is our hope that this article will provide a self-contained and useful
introduction to the topic of relativistic stellar models.
