Thisisapletelyrevisededition,withmorethafiftypagesofnewmaterialscatteredthroughout.Ikeepingwiththeconventionalmeaningofchaptersandsections,Ihavereorgaruzedthebookintotwenty-ninesectionsisevechapters.ThemaiadditionsareSectio200theLiederivativeandinteriormultiplication,twointrinsicoperationsoamanifoldtooimportanttoleaveout,newcriteriaiSectio21fortheboundaryorientation,andanewappendixoquaternionsandthesymplecticgroup.Apartfromcorrectingerrorsandmisprints,Ihavethoughtthrougheveryproofagain,clarifiedmanypassages,andaddednewexamples,exercises,hints,andsolutions.Itheprocess,everysectiohasbeerewritten,sometimesquitedrastically.Therevisionsaresoextensivethatitisnotpossibletoenumeratethemallhere.Eachchapternoweswithaintroductoryessaygivingaoverviewofwhatistoe.Toprovideatimelineforthedevelopmentofideas,Ihaveindicatedwheneverpossi-blethehistoricalorigioftheconcepts,andhaveaugmentedthebibliographywithhistoricalreferences.
黎曼曲面单值化定理是数学中美丽且重要的定理之一。它不仅给出了黎曼曲面的一个清晰的分类，而且也激发了许多新的方法。例如，它的证明激发了黎曼一希尔伯特对应和皮卡一富克斯方程，并且单值化的高维推广包含了卡拉比一丘流形。《单值化，黎曼-希尔伯特对应，卡拉比-丘流形和皮卡-富克斯方程》包括来自世界各地的专家就书名中的四个主题精心撰写的综述性文章，全面讨论了这四个主题以及它们之间的关系。《单值化，黎曼-希尔伯特对应，卡拉比-丘流形和皮卡-富克斯方程》对于初学者是一本非常有价值的入门书，也可作为其他数学家的参考书。
