Tropical geometry

Tropical geometry is a relatively new area of algebra and geometry. It can be thought of as a piecewise-linear version of algebraic geometry. The origins of tropical geometry go back to linear optimization. Nevertheless nowadays it is an active area of research in pure mathematics with connections to algebraic geometry, non-Archemean geometry/analysis, combinatorics and several other areas. I will give an introduction to this subject and towards the end try to sketch some ideas for a research in progress.