Art is long and life is short. More than four years elapsed between completion of the MS for volume I and its publication; a good deal of that time was taken up with the many tasks, often tedious, called for by the production of any decently printed book on mathematics.

An attempt has been made to speed up the process for volume II. Three quarters of it has been set directly from handwritten MS, with omission of the intermediate preparation of typed copy, so useful for bringing to light mistakes of all kinds. I have tried to detect such deficiencies on the galleys and corrected all the ones I could find there; I hope the result is satisfactory.

Some mistakes did remain in volume I in spite of my efforts to remove them; others crept in during the successive proof revisions. Those that have come to my attention are reported in the errata immediately following this foreword.

In volume I the theorem on simultaneous polynomial approximation was incorrectly ascribed to Volberg; it is almost certainly due to T. Kriete, who published it some three years earlier. L. de Branges' name should have been mentioned in connection with the theorem on p. 215, for he gave (with different proof) an essentially equivalent result in 1959. The developments in §§ A and C of Chapter VIII have been influenced by earlier work of Akhiezer and Levin. A beautiful paper of theirs made a strong impression on me many years ago. For exact references, see the bibliography at the end of this volume.