Schopenhauer is an idealist but of a rather different sort than Schelling and Hegel, so even though some of the same terms will show up as in Schelling in particular, don’t assume Schopenhauer means the same thing by them. Your assignment is divided into a number of selections that are listed below along with more specific comments.
• Selection from supplements to the first book, ch. 1, HK 448-451. This provides an introduction to Schopenhauer’s general philosophical framework. The beginning of the editors’ introduction (HK 446f) is also helpful. It is vital to notice Schopenhauer’s distinction between, on the one hand, the self or intelligence, which is an aspect of the phenomenal world, and, on the other hand, will, which he calls a thing-in-itself. The Latin phrase from Descartes (cogito ergo sum) is usually translated as “I think therefore I am.”
• Selection from §38, HK 456-460. This selection describes the general character of aesthetic pleasure. Schopenhauer uses the phrase “principle of sufficient reason” to refer to modes of explanation—of events by causal laws and of human actions by motives—and also to refer to the location of objects and events in space and time. This principle is a key manifestation of the will in the phenomenal world, so the sort of escape from the will that is found in aesthetic contemplation is associated with an escape from the principle and from the associated individuation of particular objects and of ourselves as particular subjects (something in connection with which Schopenhauer later uses the phrase principium individuationis, which means “principle of individuation”). Think about the brief comparison with dreaming (HK 458); it will reappear in Nietzsche.
• Selection from §§49-50, HK 480-486. This begins as Schopenhauer’s version of the distinction between genius and conceptual thought; but he turns, in §50, to a discussion of allegory. The value of allegory is an interesting question in its own right and it is also related to issues concerning the difference between language and pictorial representation that you’ve seen in Plotinus (in this regard, note that in his comparison allegory with hieroglyphics, Schopenhauer is probably thinking of the latter as part of an ideographic script, and thus as discursive, rather than as images that individually embody wisdom).
The attack on allegory is tied to broader issues so it is worth thinking about for discussion. Defenses of allegory against this sort of attack have been offered in recent decades (along with rejections of the sort of demand for purity in art that Schopenhauer makes here). Which side are you most sympathetic to?