Several generations of students of algebraic geometry have learned the subject from David Mumford’s fabled Red Book containing notes of his lectures at Harvard University. Their genesis and evolution are described in the preface as:

Initially notes to the course were mimeographed and bound and sold by the Harvard math department with a red cover. These old notes were picked up by Springer and are now sold as the Red book of Varieties and Schemes . However, every time I taught the course, the content changed and grew. I had aimed to eventually publish more polished notes in three volumes…

This book contains what Mumford had then intended to be Volume II. It covers the material in the Red Book in more depth with several more topics added. The notes have been brought to the present form in collaboration with T. Oda.