The second volume of Shafarevich's introductory book on algebraic varietiesand complex manifolds. As with Volume 1, the author has revised the text andadded new material, e.g. as a section on real algebraic curves. Although thematerial is more advanced than in Volume 1 the algebraic apparatus is kept toa minimum, making the book accessible to non-specialists. It can be readindependently of Volume 1 and is suitable for beginning graduate students inmathematics as well as those in theoretical physics.