This book was written for a course we teach to ?rst- and second-year college students. The style is nformal. A few problems require calculus, but thesenare identi?ed as such. Students will also need to participate while reading proofs, prodded by questions (such as, “Why?”). Many detailed examples are provided in each chapter. Since we encourage the students to draw pictures, we include many illustrations as well. Exercises, designed to teach certain concepts, are also included. These can be used as a basis for class discussion, or preparation for the class. Students are expected to solve the exercises before moving on to the problems. Complete solutions to all of the exercises are provided at the end of each chapter. Problems of varying degrees of dif?culty appear at the end of each chapter. Some problems are simply proofs of theorems that tudents are asked to read and summarize; others supply details to statements in the text. Though many of the remaining problems are standard, we hope that students will solve some of the unique problems presented in each chapter.