This textbook provides a first course in set theory suitable for final year undergraduates of mathematics. The author develops the subject from first principles and presupposes little more than an elementary grounding in logic. Throughout much attention is paid to the historical and philosophical background which illuminates the subject's development. This book differs from most textbooks of set theory by providing a particularly elegant and intuitive approach based on Scott's formulation of standard set theory in which sets are built up stage by stage. This approach has the advantage of introducing the axioms of set theory in a natural way and shows how they come to take the form they do. The text covers all the basic tools of set theory; the natural numbers, cardinals, ordinals, and the axiom of choice in some detail. It also provides an account of the representation theory of lattices and how this is closely connected with various forms of the axiom of choice.