The first thing to be said about this book is that nothing contained herein was written by Wittgenstein himself. The notes published here are not Wittgenstein's own lecture notes, but notes taken down by students, which he neither saw nor checked. It is even doubtful if he would have approved of their publication, as least in their present form. Since, however, they deal with topics only briefly touched upon in his other published writings, and since for some time they have been circulating privately, it was thought best to publish them in a form approved by their authors.