As the preface says, this book approaches the subject from two different directions: analytic and synthetic. The synthetic approach seems to contain both (1) the parts of the subject best suited to students
who know only high-school math, and (2) the parts ill-suited to those who are not "pure" mathematicians. An example of the former is a high-school-geometry-style proof that any three points on any line may be transformed to any three points on any other line via a composition of two perspectivities. An example of the latter is the projective plane that is freely generated by a configuration. The inclusion of things like this latter example is the reason why the word "foundations" is in the title; "foundations" does not mean that which should be learned before everything else; perhaps "foundations" should be defined as "that which will annoy those who want to apply projective geometry to computer graphics and which will delight `pure' mathematicians who want to know how the subject interacts with abstract algebra." The latter group will like this book and will find it very readable.

This book is short and omits some topics found in many books. Conics and polarities are not dealt with.