Significant progress has recently been made by applying tools from classical projective and algebraic geometry to fundamental problems in computer vision. To some extent this work was foreshadowed by early mathematical photogrammetrists. However the modern approach has gone far beyond these early studies, particularly as regards our ability to deal with multiple images and unknown camera parameters, and on practical computational issues such as stability, robustness and precision. These new techniques are greatly extending the scope and flexibility of digital photogrammetric systems. This tutorial provides a practical, applications-oriented introduction to the projective geometry needed to understand these new developments. No currently available textbook covers all of this material, although several existing texts consider parts of it. Kanatani's book [11] studies many computational and statistical aspects of computer vision in a projective framework. Faugeras [4] investigates the geometric aspects of 3D vision, including several of the projective results obtained by his team before 1993. The collections edited by Mundy, Zisserman and Forsyth [18, 19] summarize recent research on the applications of geometric invariants to computer vision: projective results are central to this programme.