"Preface The impetus for this book lies in our approach to teaching abstract algebra. We place an emphasis on active learning and on developing students' intuition through their investigation of examples. For us, active learning involves students--they are doing something instead of just being passive learners. What students are doing when they are actively learning might include discovering, processing, discussing, applying information, writing intensive assignments, and engaging in common intellectual in-class experiences or collaborative assignments and projects. We support all of these activities with peer review and substantial faculty mentoring. According to Meyers and Jones [2], active learning derives from the assumptions that learning is an active endeavor by nature and that different people learn in different ways. A number of reports and studies show that active learning has a positive impact on students. For example, active learning is described as a high-impact learning activity in the latest report from the Association of American Colleges and Universities' Liberal Education and America's Promise (LEAP) initiative [1]. Results of a study [3] testing the active learning findings in liberal arts education show, in part, that students who experience the type of instruction we describe as active learning show larger "value-added" gains on a variety of outcomes than their peers. Although it is difficult to capture the essence of active learning in a textbook, this book is our attempt to do just that. Our goals for these materials are several: - To carefully introduce the ideas behind definitions and theorems"--