From the reviews: "... This is one of the few mathematical books, the reviewer has read from cover to cover ...The main merit is that nearly on every page you will find some unexpected insights... " Zentralblatt für Mathematik</P>

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"... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition... which transports the reader effortlessly across the whole spectrum of algebra...Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers; certainly beginning postgraduate students would gain a most valuable perspective from it but... both the adventurous undergraduate and the established professional mathematician will find a lot to enjoy..." Math. Gazette</P>

i.r. 沙法列维奇(igor r. shafarevich)，著名代数学家。1923年6月3日生于乌克兰日托米尔 (zhytomyr)，罗蒙诺索夫国立莫斯科大学教授。早年在斯捷克洛夫数学研究所获得博士学位（师从boris delone）。对代数数论、代数几何和算术代数几何有基本的重要贡献。工作包括shafarevich-weil定理，golod-shafarevich定理、tate-shafarevich群、 grothendieck-ogg-shafarevich公式、néron-ogg-shafarevich 准则、有限可解群是有理数域上的galois群的证明、关于代数曲面的研究等。1959年获得列宁奖章。苏联（俄罗斯）科学院通讯院士和美国科学院外籍院士。

李福安，1944年1月生，浙江杭州人。1966年7月毕业于复旦大学数学系，1978年考取中国科学院数学研究所代数专业研究生（师从万哲先院士），1981年12月获理学硕士学位，1986年3月获理学博士学位。从1981年12月起在中国科学院数学研究所（数学与系统科学研究院）工作，1993年11月晋升为研究员。任algebra colloquium副主编。