The reader of this book is probably about to teach or take a "first course in proof techniques." Students are taking this course because they like mathematics, and the authors hope to keep it that way. At this point, they have an intuitive sense of why things are true, but not the exposure to detailed and critical thinking necessary to survive in the mathematical world. The authors have written this book to bridge the gap. Often, students beginning this course have little training in rigorous mathematical reasoning; they need guidance. At the end, they are where they should be; on their own. The authors aim is to teach the students to read, write and do mathematics independently, and to do it with clarity, precision, and care.