It has been twenty years since the Mathematical Society of Japan published the third edition of Encyclopedic Dictionary of Mathematics. In the meantime, mathematics has developed dramatically. Two famous problems, Fermat's Conjecture and the Poincare Conjecture, were solved affirmatively. On the other hand, the importance of mathematics for other sciences and social problems is becoming widely recognized. In this direction, Japanese mathematicians Professor Kiyoshi Ito and Koji Akaike were awarded Gauss Prize and Kyoto Prize respectively. On the occasion of the revision for the forth edition, we put much effort to include every important progress in all fields of mathematics and to show the present status of mathematics as accurate as possible. The forth edition increased in pages by almost 20 percent. In those pages we tried to maintain and reinforce the principle of the third edition that mathematics is a united body consisting of various fields organically inter-related and such relations should be emphasized in editing the dictionary. In addition, we decided to attach a disk to each printed volume. It contains the PDF files of the main texts, formulas, tables and the index of the forth edition, and of the texts of the third edition. It is hoped this new function of dictionary will provide readers with much convenience.

(Chief Editor: Akio Hattori)