It is my pleasant duty to thank here for all the help I received in the preparation of this book.

Colin Day, Director of the University of Michigan Press has permitted me to reuse material from my book Selected Topics on Polynomials published by the Press in question.

Professors Francesco Amoroso, David W. Boyd, Pierre Dèbes, Kálmán Győry, Gerhard Turnwald and Umberto Zannier have on my request read parts of the book, corrected mistakes and suggested many improvements. Chapter 1, Sections 1–3 of Chapter 3 and Section 9 of Chapter 5 have been read by U. Zannier. He has also written a very important appendix ‘Proof of Conjecture 1’. Chapter 2 has been read by G. Turnwald, who has also made most useful comments on Appendix A. Section 4 of Chapter 3 has been read by D.W. Boyd, Sections 1, 2, 3 of Chapter 4 by F. Amoroso, Section 4 of Chapter 5 and Sections 1–8 of Chapter 5 by P. Dèbes, finally Chapter 6 by K. Győry. In addition the whole book has been generously proofread by Jadwiga Lewkowicz and Andrzej Mąkowski, and the beginning of Chapter 1 by Andrzej Kondracki. I have also profited by advice from Dr. Michael Zieve concerning Section 5 of Chapter 4, from Professors Dieter Geyer, David Masser and Peter Roquette concerning Section 4 of Chapter 4 and from Professors Zbigniew Ciesielski, Piotr Mankiewicz, Aleksander Pełczyński and Dr. Marcin Kuczma concerning Appendix G.