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.

　　本書為英文版。

G. H. Hardy (1877－1947 ) 享有世界聲譽的數學大師，英國分析學派的創始人之一。數學貢獻涉及解析數論、調和分析、函數論等方麵。培養和指導瞭包括印度數學奇纔拉馬努金和我國數學傢華羅庚在內的眾多數學大傢。

J. E. Littlewood（1885—1977）著名英國數學傢。任劍橋大學教授多年，他也是英國分析學派的重要建立者，與G. H. Hardy長期閤作取得瞭豐碩的成果。在數論和分析學等方麵貢獻很大。

G. Pólya（1887—1985）著名數學傢和數學教育傢。美國國傢科學院院士，美國藝術和科學學院院士。長期擔任斯坦福大學教授。其數學研究涉及復變函數、概率論、數論、數學分析、組閤數學等眾多領域。他撰寫的《怎樣解題》、《數學的發現》、《數學與猜想》等闡述解題方法的著作有世界性影響。