Vortex motion as an essential ingredient of the universe structure has attracted attention of researchers and philosophers from ancient to modern times. But the mathematical description of it has begun in XIX century with works of Hermann Helmholtz and Gustav Kirchoff. This book is devoted to mathematical problem of integrable vortex dynamics as a pole dynamics in complex plane. Starting from basic notions of a fluid motion the authors cover the Kirchhoff equations, C-integrable models and time dependent holomorphic Schrodinger equation. Intriguing relations with motion of magnetic vortices, the Chern-Simons field theory, Calogero-Moser systems, Burgers’ hierarchy and the space-time noncommutativity are presented in a systematic way. The book is self consistent and pedagogically written as an introduction to the subject for students at undergraduate and graduate level from science and engineering specialties. Also it could be a valuable source for researchers in the field.

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