The concept of Riemann surfaces was introduced in Riemann's thesis,
and the moduli space of Riemann surfaces was defined by Riemann in
a masterpiece a few years later. Due to a broad connection with
many subjects in mathematics and physics, Riemann surfaces and
their moduli spaces have been intensively studied and should
continue to attract attention in years to come. Recently, there has
been an explosion of interest in and work on tropical algebraic
curves-analogues of algebraic curves over the complex numbers and
hence of Riemann surfaces. This book is an accessible introduction
to all these topics, with special emphasis given to their many
connections with subjects such as algebraic geometry, complex
analysis, hyperbolic geometry, topology, geometric group theory,
and mathematical physics.
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