The four pillars of geometry / John Stillwell

The pillars of the title are, in order of presentation: Euclidean construction and axioms, coordinates and vectors, projective geometry, and transformations and non-Euclidean geometry. There are two chapters on each topic: the first concrete and introductory, the second more abstract. The writing style is both student-friendly and deeply informed. The pleasing brevity of the book, together with the inclusion of computational detail devoid of phrases such as, "The reader can easily show…'', makes the book especially suitable as an introduction to geometry for the large and critically important population of undergraduate mathematics majors who are, perhaps, not destined for elite doctoral programs. Each chapter concludes with a well-written discussion section that combines history with glances at further results. There is a good selection of thought-provoking exercises. (MathSciNet)