 This is a most unusual book ... Every working mathematician of course knows the difference between a lifeless chain of formalized propositions and the " feeling " one has ( or tries to get ) of a mathematical theory , and will probably agree that helping the student to reach that " inside " view is the ultimate goal of mathematical education ; but he will usually give up any attempt at successfully doing this except through oral teaching . The originality of the author is that he has tried to attain that goal in a textbook , and in the reviewer 's opinion , he has succeeded remarkably well in this all but impossible task . Most readers will probably be delighted ( as the reviewer has been ) to find , page after page , painstaking discussions and explanations of standard mathematical and logical procedures , always written in the most felicitous style , which spares no effort to achieve the utmost clarity without falling into the vulgarity which so often mars such attempts . 
