This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Ric

Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to s

Tropical geometry is young field of mathematics that connects algebraic geometry and combinatorics. It considers "combinatorial shadows" of classical algebraic

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tr

These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of