Rhetorical knowledge can be broadly defined as knowing how rhetoric works and how to use it.
While one common use of the word rhetoric is to mean false or meaningless speech - "I've had enough of your rhetoric," said Aunt May - a more traditional definition (given by J.A. Cuddon and M.A.R. Habbib in The Penguin Dictionary of Literary Terms and Literary Theory, "Rhetoric") is
the art of using language for persuasion, in speaking or writing; especially in oratory.
Note: Rhetoric does not have to involve language. For example, visual rhetoric (both moving and still images), aural rhetoric (sound and music), and non-verbal rhetoric (sign language, body language) are other rhetorical forms that don't necessarily involve words. In the past two decades, the term digital rhetoric has increasingly been used to describe forms of communication that occur online.
Ultimately, any communication with an audience can constitute an act of rhetoric.
Where is rhetoric? Well, it's all around us: every ad we watch on television, every website we visit, every sign on a billboard or flyer for an event on campus, when your friend tries to convince you to go see a movie: these are all different acts of rhetoric. When used effectively, rhetoric enables us to persuade others to act or believe in a different way, like a coach motivating his team at halftime, a parent telling their kid they did a good job, or a leader trying to convince voters to support their policies.
How old is rhetoric? While rhetoric itself is probably as old as human communication, formal study of rhetoric began in the ancient world (see for example Plato's disputes with the rhetorical teachings of the Sophists, Aristotle's foundational work the Rhetoric, or this book on even older traditions) and continues into the present day.
Can you recommend some new(er) books for learning about rhetoric? Sure! Try these.
Understanding Rhetoric : a graphic guide to writing by 
Classical Rhetoric for the Modern Student by 
Rhetorical Style : the uses of language in persuasion by 
Rhetoric, Through Everyday Things by For the related topic of prose style, you may wish to consult the Prose Style Analysis box on the Criticism & Theory page of this guide.
An important step in creating effective rhetoric is to choose an effective message to deliver. Yet our message can be brilliant yet still not succeed in accomplishing our goals if it fails to address our audience(s) effectively, or if we (as deliverers of the message) do not establish enough credibility with the audience in order to persuade them.
"Rhetorical Tetrahedron" by ChloeGui, CC BY-SA 4.0, via Wikimedia Commons
In an influential model of communication first proposed by the rhetorician Lloyd Bitzer in the 1950s, each of these three factors combines with the context of any given situation to create what Bitzer called the rhetorical situation. The rhetorical situation is often represented as a tetrahedron consisting of the text, the communicator, and the audience, each of which are shaped by the central context.
Overviews of each element of the rhetorical situation can be found in Chapter 5 of Andrea E. Lunsford's The Everyday Writer, 5th edition (available to consult on the library's Ready Reference Shelf.)
In section 5c of this chapter, Lunsford discusses how to decide on an appropriate message, while in section 5d Lunsford discusses how to determine the purpose and stance in the context of academic writing which will give us the most credibility in the eyes of our audience. In section 5e, Lunsford describes ways of analyzing our audience, including discussions of the differences between informal and informal audiences and questions to consider in order to select appropriate language for our audience. In section 5f, Lunsford talks about other factors to consider that shape the writing context, such as the time available to complete the assignment, the desired length, the genre, medium, and format, and the appropriate tone and style.
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