Despite dissent in many quarters, Piaget's epistemology and the developmental psychology derived from it remain the most powerful theories in either field. From the beginning, Piaget's fundamental epistemological notion was that all knowledge is rooted in action, and for a long time, he identified action with transformation. What is known is that which remains constant under transformatory action. This book represents a fundamental reformulation of that point of view. Alongside transformatory schemes, Piaget now presents evidence that nontransformatory actions -- comparisons that create morphisms and categories among diverse situations constitute a necessary and complementary instrument of knowledge. This work aims to elucidate that insight experimentally and theoretically and to understand the developmental interaction of comparing and transforming as knowledge is constructed. This first English translation of Piaget's work includes studies of children's understanding of geometric forms, machines, and abstract concepts. It contains a clear statement of his mature position on continuity with biology as well as with the history of ideas.