The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results.
From the reviews:
In this expansive volume, Shult (Kansas State Univ.) attempts to provide a thorough, self-contained characterization of geometries of Lie type by means of local axioms on points and lines. There is enough material here for several semester-long graduate courses; alternatively, the book could be used as a reference work. Shult makes every effort to remain chatty and intuitive while ensuring precision and detail. Summing Up: Recommended. Graduate students and researchers. (S. J. Colley, Choice, Vol. 48 (11), July, 2011)
This book presents characterizations of the classical geometries of Lie type by axioms on points and lines; it is a teaching book with detailed proofs, written for beginning graduate students. Most chapters end with a set of exercises . The whole book shows the author's love of incidence geometry and of teaching. (Theo Grundhöfer, Mathematical Reviews, Issue 2011 m)
Shult has designed the book as a self-contained resource for a graduate student who plans to pursue research in this area. the book gives detailed proofs and offers exercises at the end of each chapter, organized by topic. geometrically inclined readers will wish to illustrate the text, in addition to working through the official exercises. the intensity of detail and sparsity of illustrations make it more suitable as a handbook for experts . (Ursula Whitcher, The Mathematical Association of America, July, 2012)