Simon Gindikin did an excellent job in this new edition of his book. I got acquainted with his research not too long ago when reading an essay on Penrose's Twistor theory in the "Mathematical Intelligencer" by Springer dating from early 80's.Eventually I found out the first edition of his book, which was already quite delightful.The book, besides being filled with witty historical facts, contains also a few interesting problems to improve one's mathematical culture.I'm particulary kind of the chapter on Huygens and his mechanical works,Poincare's ideas on non-euclidean geometry and finally and the above mentioned article on twistor theory(which could be included on a course on analytical/projective geometry, example).As my usual cliche, "Two thumbs up!".