These Lecture Notes are an expanded version of the Fermi Lectures Atiyah gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978. In all cases he was addressing a mixed audience of mathematicians and physicists and the presentation had to be tailored accordingly. Throughout, Atiyah presented the mathematical material in a somewhat unorthodox order, following a pattern which he felt would relate the new techniques to familiar ground for physicists.
The main new results presented in the lectures, namely the construction of all multi-istanton solutions of Yang-Mills fields, is the culmination of several years of fruitful interaction between many physicists and mathematicians. The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his “twistor programme” were ideally suited to the study of the Yang-Mills equations. The instanton problem was then seen to be equivalent to a problem in complex analysis and to one in algebraic geometry. Using the powerful methods of modern algebraic geometry it was not long before the problem was finally solved.

早在1959年，任朗、袁炳南二位先生就按1948年俄文第二版将本书译为中文出版，深受国内广大读者欢迎。半个多世纪以来，本书俄文原版历经数次修改和增补，和最初的版本相比篇幅已大为增加，全书的内容（特别是有关引力场理论的内容）多有更新，迫切需要出版包括这些修改和增补的新的中译本。这次的翻译是在任、袁二位先生原译本的基础上，按2006年俄文第八版进行的。
新译本的1—9章和12章由国家天文台邹振隆先生依据俄文第八版并参考英文第四版进行了校订。第10,11,13,14章的增补部分、序言和索引由鲁欣依俄文第八版版翻译，亦由邹振隆先生进行了校订。
北京师范大学物理系裴寿镛和赵峥二位先生，他们在出版前分别审读了1—9章和10—14章的译稿，提出了许多宝贵的意见，使得译稿更加完善。北京大学力学系李植老师和中国科学院理论物理研究所刘寄星先生依据俄文版对序言译文作了修改。
此卷采用的是Latex排版，纸张的手感比同系列已出版的另外6卷更好。还值得一提的是，在历时近一年的时间里，编辑通过朗道集结号微博与读者充分互动，从公式的排版，到物理名词该如何翻译，都听取了读者了建议，部分读者通过朗道系列图书的微博对部分译稿进行了试读，还有个别读者热心地通读了全稿，从科学性和文字两方面均提出了很多中肯的修改建议。本书即是“云编辑”概念提出后的第一本出版物。相信读者拿到书一定会有物有所值的感觉。朗道集结号希望从此将“云编辑”概念继续发扬下去，出版出更多的精品，以飨读者。受专业水平和语言水平的限制，译文中错误和不当之处在所难免。恳切地希望各位读者发现后批评指正，以便重印时修改。