Schopenhauer is widely known for being influenced by Buddhism's claim that life is suffering and for in turn influencing Nietzsche, but his major influence is Kant.
On the Fourfold Root of the Principle of Sufficient Reason, was originally written (in 1813) as S's dissertation but was later expanded and clarified for proper publication (in 1847). He considered this his core work which you need to read to understand any of the rest of it. Whereas most of the other post-Kantians of note (like Hegel, Nietzsche, and Sartre) ignore or deny the existence of Kant's "thing-in-itself," i.e. the objective thing prior to our cognizing it, Schopenhauer makes it the core of his philosophy, connecting it with the "will to live." So that would be the "will" part in his more famous book The World as Will and Representation, which is very large and will have to wait for a future episode for us to look into. The essay we will be reading covers more of the "representation" part of this, with the principle of sufficient reason being the way in which we understand things: we look for their cause, for the reason why the thing is there and is the way it is. Schopenhauer reorganizes Kant's analysis of our faculties of knowledge by elaborating four classes of explanation that fall under this principle of sufficient reason, which you can preview here if you'd like.