TITLE: Comprehensive and self-contained treatment of Algebraic Geometry using Functor of Points approach
QUESTION [15 upvotes]: The book everyone seems to use to study Algebraic Geometry is Hartshorne's book. However, I hear a good number of people saying that this book totally misses the functorial point of view. Hence, could you please recommend a good source to learn AG using the Functor of Points approach?  Thanks!!

REPLY [8 votes]: Dear Brian, it seems that algebraic geometers who adopt your favoured approach are essentially specialists in algebraic groups. 
My favourite example would be Jantzen's Representations of Algebraic groups", Academic Press 1987, in which all of Chapter 1 (18 pages) is devoted to the functor approach  you require. Let me emphasize that Jantzen doesn't limit himself to affine schemes nor to group schemes. He considers  completely general schemes defined as local functors admitting an open covering (in the functor sense!) consisting of affine schemes . I am sure you'll love the ingenious but natural  definitions of open subfunctor, closed subfunctor, base change ... introduced in this meaty chapter: good luck!