This is an introductory chapter that defines and clarifies some notions that will be fundamental to the rest of the book. First, liberalism is seen as a theory looking for an answer to the question ‘how to live together?’ in condition of deep diversity. Second, diversity is considered as a fact marking contemporary society, a fact to which liberalism has to find an answer. This chapter distinguishes between comprehensive and political liberalism, and between pro-autonomy and pro-toleration liberalism. Combining the two distinctions, one obtains four kinds of liberal theories: comprehensive pro-autonomy (hereafter CA), comprehensive pro-toleration (hereafter CT), political pro-autonomy (hereafter PA), and political pro-toleration (hereafter PT). These four theories, the author contends, offer a wide overview of the contemporary academic debate. This chapter also contains a schema of this book.