The title “Tangency and Duality over Arbitrary Fields" was given by Wallace to the article in which he pioneered the study of the similarities and differences that appear in the indicated theory, a basic topic in projective algebraic geometry, when the characteristic p of the ground field is allowed to become positive. The title is also an apt choice for the present work. However, the words "over Arbitrary Fields" were dropped for two reasons: First, the subject has matured to the point where it can, fairly, go without saying that p will be arbitrary. Second and more important, the similarities and differences attendant to p are secondary to the geometry itself. The bulk of material ia, moreover, characteristic free, and many of the special considerations required when p > 0 highlight features of geometry over the complex numbers that are sometimes taken for granted. A case in point is provided by the central notion of reflexivity. In most situtations, instead of assuming p= 0 , it suffices to asaume that the principal varieties are reflexive. A major issue then, when p> 0, is to find useful conditions guaranteeing reflexivity.