  This paper is to serve as a key to the projective (homogeneous) model
developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain
the underlying concepts in a simple language and give plenty of examples. It is
targeted to physicists and engineers and the emphasis is on explanation rather
than rigorous proof. The projective model is based on projective geometry and
Clifford algebra. It supplements and enhances vector and matrix algebras. It
also subsumes complex numbers and quaternions. Projective geometry augmented
with Clifford algebra provides a unified algebraic framework for describing
points, lines, planes, etc, and their transformations, such as rotations,
reflections, projections, and translations. The model is relevant not only to
Euclidean space but to a variety of homogeneous metric spaces.
