An argumentation and debate textbook for the digital age. Composing Arguments combines traditional and contemporary theory with the online argument mapping tool Debategraph. This edition covers basic concepts regarding the definition and composition of arguments. The theory focuses on informal logic and is heavily influenced by Stephen Toulmin and Ludwig Wittgenstein, but traces the roots of argumentation theory to Aristotle. The first half of the textbook includes explanations of the syllogism, enthymeme, and the Toulmin model. Additionally, there are images of argument maps to illustrate the concepts, as well as exercises for students to use for studying. The second half of the textbook has step-by-step instructions for using Debategraph, complete with assignments that have been tried and tested in the classroom. This book represents the next step in argumentation and debate instruction. Use it for the class, or for instruction for competitive debate.