This graduate level text on first-order logic highlights the importance of this area as well as the abundance of results and some applications. The best-known of textbooks originated in an earlier era, and despite frequent updating by their authors, they reflect a general view and a particular approach that is less adequate today. The addition of "metatheory" clarifies that this is not a textbook in which the emphasis is on the basics such as formalizing English sentences and learning the use of one or another calculus. This textbook takes a fresh look at the current state of first-order logic, and integrates newer results with a reevaluated stock of earlier ones.