In spirit, this book is closer to Elements de Geometrie Algebrique (EGA) than the existing textbooks on algebraic geometry. It prvides an introduction to schemes, formal schemesc coherent sheaves, and their cohomologies. The prerequisites for reading this book is the knowledge of commutative algebra up to the level of Ateyah-Macdonald's book. The material on algebraic geometry covered in this book provides adequate preparation for reading more advanced books such as Seminaire de Geometrie Algebrique (SGA).

In this book we study the cohomology of coherent sheaves on schemes. An excellent textbook on this topic is [Hartshorne]. But in Hartshorne's book, many important theorems which hold for proper morphisms are proved only for projective morphisms. Moreover, Hartshorne does not say much about the technique of spectral sequences. The main purpose of this book is to fulfil this need. Of course, everything in this book is contained in Grothendieck's [EGA] (see Bibiography [4]). I hope this book can make the wonderful ideas of Grothendieck which are hidden in the voluminous [EGA] more clear. To make the book self-contained, I include many materials which are treated nicely in [Hartshorne]. So t...