The object of the present book is to provide a text for a one-year course, essentially following the recommendations of the Committee on the Undergraduate Program in Mathematics of the Mathematical Association of America. The seven chapters cover most of the basic material listed in the first seven paragraphs of the CUPM recommendations, together with as much optional material as can be naturally absorbed. Although this book is designed ultimately for pregraduate preparation, it seems more suitable (as do the CUPM recommendations) for today's first-year graduate students than for upper-division undergraduates, in view of the present mathematical level of the colleges.