This textbook, aimed at advanced undergraduate or beginning
graduate students in mathematics, introduces both the theory of
Riemann surfaces, and of analytic functions between Riemann
surfaces. The first half of the book describes the basic theory,
the second half develops the theory of harmonic and subharmonic
functions on a Riemann surface, and culminates with a detailed
proof of the famous Uniformisation Theorem and some of its
applications to Riemann surface theory. The book is a major
revision of the author's earlier 'Primer', with new chapters and
more exercises and examples.
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