This is the first extant book of Roman elegy (Gallus, as ever, is a missing presence), and for most readers it defines the genre. Because we have three (at least) more books of Propertius, it is easy to misunderstand the title: it means "single book" not "first book", and it was clearly intended to stand alone--that Propertius retroactively modified this, particularly at the end of Book 3, is not relevant.

The most important questions to consider are fairly straightforward, even if the answers are not.

1. What kind of poetry is P. defining/creating in this book? What is the relationship between love-elegy (as we call it) and earlier poetry, both Roman (Eclogues, comedy) and Greek (Callimachus, amatory epigrams)?

2. How do the opening poems of the book define the elegiac relationship? Who is Cynthia, what is she? And how does "Cynthia" define the relationship between poet and poem?

3. What kind of relationship is "love" in this poetry? What are the main images/metaphors for erotic passion, and how do they affect the reader's understanding of the relationship (and the poetry)?

4. How does Propertius use myth? Look particularly at poems 1 and 3.

5. Even though you are not reading the whole book, the selections assigned allow you to see pretty clearly what its shape is (although if you have time, you should also read poem 20). The same question applies as with the poetic books of Vergil and Horace: how does this work as a narrative? And, above all, what is the relationship between the Cynthia poems and the final two poems of the book? What do the final poems (and poem 6) imply about the relationship between the book and the world?

Bibliography:

There are some excellent introductions to Propertius, above all

S. Commager, A Prolegomenon to Propertius (Cincinnati, 1974)

M. Hubbard, Propertius (London, 1974)

H. Tränkle, Die Sprachkunst des Properz und die Tradition der lateinischen Dichtersprache (Wiesbaden, 1960) is a superb philological study of poetic diction.

Some other studies of Propertius' poetics that are relevant here are:

D. O. Ross, Backgrounds to Augustan Poetry (Cambridge, 1975)--again.

M. Wyke, "Written Women: Propertius' Scripta Puella," JRS 77 (1987) 47-61

And, having given up all modesty, I add my own article, which may give some explanation of the nature of Roman Alexandrianism (at least in my interpretation):

J. Zetzel, "Poetic Baldness and its Cure," Materiali e Discussioni 36 (1996) 73-100.