I have the privilege of teaching the graduate course "Introduction to New Testament Exegesis" every two years. This year, I've decided to shake up my normal way of teaching the class and add in a part on "New Testament Rhetoric," which I've begun dabbling in, for better of for worse!
Now, "rhetoric" itself is difficult to define, and scholars do not always agree amongst themselves. Carl Joachim Classen provides us a good starting point: "The deliberate, calculated use of language for the sake of communicating various kinds of information ini the manner intended by the speaker (and the theory of such a use)" (Classen 2002, 45). In a nutshell, the study of rhetoric assumes that how an author says something is important in addition to what he or she says.
In modern scholarly treatments on NT rhetoric, the focus is often on macro-rhetoric, or the overall structure of a letter and its persuasive power. This was popularized with Hans Dieter Betz's commentary on Galatians (1979), where he mapped the structure of the epistle according to formal Greco-Roman conventions. This, however, is highly controversial, as seen in a recent issue of Bulletin for Biblical Research which included a debate between Ben Witherington + Jason Myers vs. Stanley Porter on this topic (see below). Interestingly, out of all the New Testament epistles besides Galatians, 2 Peter is perhaps the most likely to be analyzed in terms of formal Greco-Roman rhetoric (ever since Duane F. Watson published his highly influential monograph in 1988).
I'm a bit more interested in "micro-rhetoric," which deals with the minutiae such as word-order, word-play, alliteration, etc., as well as how such items impact or illuminate the social relationship between the author and his or her audience. To a certain degree rhetorical studies and discourse analysis overlap here, though virtually nobody that I know of discusses how the two intersect (except, intriguingly, Alan Kam-Yau Chan's 2016 monograph on Melchizedek Passages in the Bible, though all too briefly).
Anyways, here are some resources I've found especially helpful for studying the topic. All of them are reasonably priced (we're not talking inaccessible $100 monographs here). I should also mention that I will require my students to read my Doktorvater, David Alan Black's Linguistics for Students of New Testament Greek, which has sections on both rhetoric and discourse analysis.
Helpful resources:
Black, C. Clifton. The Rhetoric of the Gospel: Theological Artistry in the Gospels and Acts, 2nd ed. Louisville: Westminster John Knox, 2013. C. Black's essay in the 2010 book Hearing the New Testament: Strategies for Interpretation (2nd ed.) is also helpful.
Bulletin for Biblical Research 26 no. 4 (2016), with an initial article by Stanley E. Porter, a response by Jason A. Myers and Ben Witherington, and a rejoinder by Porter. For more on Porter vs. Witherington, see The Journal of the Evangelical Theological Society 55 no. 2 (2012) for a critique by Porter of Witherington's work in social-rhetorical criticism, and then JETS 58 no. 1 (2015) for Witherington's defense of analyzing NT texts in light of Greco-Roman rhetoric.
Classen, Carl Joachim. Rhetorical Criticism of the New Testament. Boston: Brill Academic, 2002.
Kennedy, George A., trans. and ed. Invention and Method: Two Rhetorical Treatises from the Hermogenic Corpus. Writings from the Greco-Roman World. Atlanta: Society of Biblical Literature, 2005. This is one of the key ancient sources on rhetoric, and we can thank Dr. Kennedy for providing a modern translation (I've tried to translate parts of this on my own from TLG; I didn't fare too well!). The reader should also be aware that Aristotle's The Art of Rhetoric is a much earlier Greek source on the topic.
Kennedy, George A. New Testament Interpretation through Rhetorical Criticism. Chapel Hill, NC: University of North Carolina Press, 1984.
Martin, Troy W., ed. Genealogies of New Testament Rhetorical Criticism. Minneapolis: Fortress, 2014. Personally, I found this book very helpful in explaining the various views out there on rhetorical criticism in NT studies.
Muilenburg, James. "Form Criticism and beyond." Journal of Biblical Literature 88 no. 1 (1969): 1-18. Notwithstanding its somewhat misleading title, this article (originally a presidential address) is considered a landmark source that reignited interest in rhetorical criticism in biblical studies.
Watson, Duane Frederick. Invention, Arrangement, and Style: Rhetorical Criticism of Jude and 2 Peter. SBLDS 104. Atlanta: Scholars, 1988.
Witherington, Ben, III. New Testament Rhetoric: An Introductory Guide to the Art of Persuasion in and of the New Testament. Eugene, OR: Cascade, 2009.
Wuellner, Wilhelm. "Where Is Rhetorical Criticism Taking Us?" Catholic Biblical Quarterly 49 no. 3 (1987): 448-63. Wuellner helped facilitate a movement to pay more attention to the social dimensions of rhetoric.
Warning! Closing theological digression alert! As a final point, for those of us that believe in the inerrancy of Scripture, we must take the issue of rhetoric a step farther: how the Holy Spirit says something is relevant, in addition to what He said in Scripture. More than just the choice of words, such things as structure, word-order, word-play, etc., are all part of the inspiration of the original documents. Which is why any claim for perfection of a particular translation actually diminishes the doctrine of inerrancy: The Holy Spirit himself inspired the alliteration in Hebrews 1:1, alliteration which is lacking in the King James (and almost all English translations). This means that no matter how solid a translation might be on Hebrews 1:1 (and the KJV translators did an excellent job here), if it did not alliterate in the target language, it is not perfectly preserving all that the Holy Spirit inspired. End of theological digression!