These notes present a polished introduction to tropical geometry
and contain some applications of this rapidly developing and
attractive subject. It consists of three chapters which complete
each other and give a possibility for non-specialists to make the
first steps in the subject which is not yet well represented in the
literature. The notes are based on a seminar at the Mathematical
Research Center in Oberwolfach in October 2004. The intended
audience is graduate, post-graduate, and Ph.D. students as well as
established researchers in mathematics.
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