This paper explores the concept of finitistic dimension and its generalization to semi-primary rings. It begins by introducing the finitistic global dimension, which is defined by restricting the supremum of projective dimensions to finitely generated modules of finite projective dimension. The paper then presents a general investigation of these dimensions, characterizing rings for which various of these dimensions vanish or equal one. A key result is the noncommutative extension of Kaplansky's theorem, which characterizes commutative rings with vanishing finitistic dimension. The paper also discusses the relationship between various homological dimensions, including the global dimension, weak global dimension, and injective dimension. It provides a characterization of rings where these dimensions vanish or are bounded, and includes examples illustrating these results. The paper further explores the concept of left perfect rings, which are rings where every left module has a projective cover. It shows that left perfect rings have equivalent properties, including the vanishing of weak and projective dimensions for all modules. The paper then presents a detailed proof of Theorem P, which characterizes rings where the Jacobson radical is left T-nilpotent and the quotient ring is semi-simple. This theorem is shown to be equivalent to the ring being left perfect. The paper also discusses the duality between modules and their duals, and applies this duality to study homological dimensions. The paper concludes with applications to homological dimensions, including the finitistic dimension and its properties in Noetherian rings. It presents several theorems and corollaries, including the characterization of rings with finitistic dimension zero, and the relationship between injective modules and their envelopes. The paper also discusses the implications of these results for semi-primary rings and the conditions under which certain homological dimensions vanish.This paper explores the concept of finitistic dimension and its generalization to semi-primary rings. It begins by introducing the finitistic global dimension, which is defined by restricting the supremum of projective dimensions to finitely generated modules of finite projective dimension. The paper then presents a general investigation of these dimensions, characterizing rings for which various of these dimensions vanish or equal one. A key result is the noncommutative extension of Kaplansky's theorem, which characterizes commutative rings with vanishing finitistic dimension. The paper also discusses the relationship between various homological dimensions, including the global dimension, weak global dimension, and injective dimension. It provides a characterization of rings where these dimensions vanish or are bounded, and includes examples illustrating these results. The paper further explores the concept of left perfect rings, which are rings where every left module has a projective cover. It shows that left perfect rings have equivalent properties, including the vanishing of weak and projective dimensions for all modules. The paper then presents a detailed proof of Theorem P, which characterizes rings where the Jacobson radical is left T-nilpotent and the quotient ring is semi-simple. This theorem is shown to be equivalent to the ring being left perfect. The paper also discusses the duality between modules and their duals, and applies this duality to study homological dimensions. The paper concludes with applications to homological dimensions, including the finitistic dimension and its properties in Noetherian rings. It presents several theorems and corollaries, including the characterization of rings with finitistic dimension zero, and the relationship between injective modules and their envelopes. The paper also discusses the implications of these results for semi-primary rings and the conditions under which certain homological dimensions vanish.