It is often really difficult to trace the origin of a familiar inequality. It is quite likely to occur first as an auxiliary proposition, often without explicit statement, in a memoir on geometry or astronomy; it may have been rediscovered, many years later, by half a dozen different authors; and no accessible statement of it may be quite complete. We have almost always found, even with the most famous inequalities, that we have a little new to add. We have done our best to be accurate and have given all references we can, but we have never undertaken systematic bibliographical research. We follow the common practice, when a particular inequality is habitually associated with a particular mathematician's name; we speak of the inequalities of Schwarz, HSlder, and Jensen, though all these inequalities can be traced further back; and we do not enumerate explicitly all the minor additions which are necessary for absolute completeness. We have received a great deal of assistance from friends. Messrs G. A. Bliss, L. S. Bosanquet, R. Courant, B. Jessen, V. Levin, R. Rado, I. Schur, L. C. Young, and A. Zygmund have all helped us with criticisms or original contributions. Dr Bosanquet, Dr Jessen, and Prof. Zygmund have read tho proofs, and corrected many inaccuracies. In particular, Chapter III has been very largely rewritten as the result of Dr Jessen's suggestions. We hope that the book may now be reasonably free from error, in spite of the mass of detail which it contains.

　　本书为英文版。

G. H. Hardy (1877－1947 ) 享有世界声誉的数学大师，英国分析学派的创始人之一。数学贡献涉及解析数论、调和分析、函数论等方面。培养和指导了包括印度数学奇才拉马努金和我国数学家华罗庚在内的众多数学大家。

J. E. Littlewood（1885—1977）著名英国数学家。任剑桥大学教授多年，他也是英国分析学派的重要建立者，与G. H. Hardy长期合作取得了丰硕的成果。在数论和分析学等方面贡献很大。

G. Pólya（1887—1985）著名数学家和数学教育家。美国国家科学院院士，美国艺术和科学学院院士。长期担任斯坦福大学教授。其数学研究涉及复变函数、概率论、数论、数学分析、组合数学等众多领域。他撰写的《怎样解题》、《数学的发现》、《数学与猜想》等阐述解题方法的著作有世界性影响。