An ideal text for an advanced course in the theory of complex
functions, this book leads readers to experience function theory
personally and to participate in the work of the creative
mathematician. The author includes numerous glimpses of the
function theory of several complex variables, which illustrate how
autonomous this discipline has become. In addition to standard
topics, readers will find Eisenstein's proof of Euler's product
formula for the sine function; Wielandts uniqueness theorem for the
gamma function; Stirlings formula; Isssas theorem; Besses proof
that all domains in C are domains of holomorphy; Wedderburns lemma
and the ideal theory of rings of holomorphic functions; Estermanns
proofs of the overconvergence theorem and Blochs theorem; a
holomorphic imbedding of the unit disc in C3; and Gausss expert
opinion on Riemanns dissertation. Remmert elegantly presents the
material in short clear sections, with compact proofs and
historical comments interwoven throughout the text. The abundance
of examples, exercises, and historical remarks, as well as the
extensive bibliography, combine to make an invaluable source for
students and teachers alike
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