This is supposedly a review book. Yet I think it is one of the best books on the subject. It is elementary, and might not cover all the latest advances, yet it has a wealth of examples, beautiful explanations, and a very nice assortment of subjects. I particularly liked his lozenge diagram approach to methods of integration, his concise and lucid explanation of the Euler-Maclaurin sum formula, applications of the sum calculus, and clear parallels to standard calculus (ininitesimal) throughout. You can't do much better than this well-written text for basics of finite differences.