Abstract
The primary goal of this dissertation is to discuss new developments in the finitistic dimension conjecture from the point of view of homological invariants. Using the tools from representation theory of associative algebras, or quiver representations, category theory, and combinatorics, we introduce new invariants for the finitistic dimension conjecture called the sub-derived delooping level and derived delooping level. We present several applications including comparing our new invariants with previous invariants called the $\phi$-dimension and $\psi$-dimension, creating a symmetry condition of the derived delooping level as another sufficient condition for the conjecture, and lastly investigating the properties of delooping level and derived delooping level under taking tensor products of algebras and over right and left serial monomial algebras.