In this volume, the editor presents reprints of most of the fundamental papers of Gian-Carlo Rota in the classical core of cominatorics. These include Part I, III, IV, VI and VII of the Foundation series on Mobius fuction, polynomials of binomial type, counting in vector spaces, generating functions and symmetric functions. Also reprinted are papers which are derived or related to the themes explored in these central papers. Rota's work, starting with the paper, "On the Foundations of Combinatorial Theory: I - Theory of Mobius Functions" (1964) has revolutionized the way we approach combinatorics; this volume is intended to be an introduction to his way of thinking about that subject. Kung has provided a substantial amount of new material on the impact that Rota's papers have had on combinatorics. Extensive survey articles are included in each chapter to guide the reader, both to the reprinted papers and to the works of others which have been inspired by these papers. There are also four prefatory essays describing Rota's special influence on combinatorics, particularly at the historical Bowdoin conference in 1970. This book is intended for experts as well as beginning graduate students (particularly as a source for research problems).