This text is an attempt to cover some of the salient features of variable complex function theory. The approach is analytical, as opposed to geometric, but the methods of the three principal schools (Cauchy, Riemann and Weierstrass) are developed. The book goes into several topics deeply (eg, convergence theory and plane topology) and chapter notes give the sources of the results, trace lines of subsequent development, make connections with other topics, and offer suggestions for further reading. These notes are keyed to a bibliography of over 1300 books and papers.

Review:

"This is, I believe, the first modern comprehensive treatise on its subject. The author appears to have read everything, he proves everything, and he has brought to light many interesting but generally forgotten results and methods. The book should be on the desk of everyone who might ever want to see a proof of anything from the basic theory...." (SIAM Review)

" ... An attractive, ingenious, and many time[s] humorous form increases the accessibility of the book...." (Zentralblatt f�r Mathematik)

"Professor Burckel is to be congratulated on writing such an excellent textbook.... this is certainly a book to give to a good student [who] would profit immensely from it...." (Bulletin London Mathematical Society)

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