Preface -- The subject commonly called "Advanced Calculus" means different things to different people. To some it essentially represents elementary calculus from an advanced viewpoint, i.e., with rigorous statements and proofs of theorems. To others, it represents a variety of special advanced topics which are considered important but which cannot be covered in an elementary course. --- In this book an effort has been made to adopt a reasonable compromise between these extreme approaches which, it is believed, will serve a variety of individuals.