Introduction to Tropical Geometry

[2][3] Although past work in the area has studied it through methods of enumerative combinatorics, this book instead is centered around explicit calculations related to the tropicalization of classical varieties.

Its first introduces the subject and gives an overview of some important result, after which the second chapter provides background material on non-Archimedean ordered field, algebraic varieties, convex polytopes, and Gröbner bases.

Chapter four studies tropical connections to the Grassmannian, neighbor joining in the space of metric trees, and matroids.

[1][3] Reviewer Patrick Popescu-Pampu claims that even though it is a graduate-level book series, undergraduates with a sufficient background in algebraic geometry should be able to access it.

[1] Reviewer Michael Joswig concludes that Introduction to Tropical Geometry "will become a standard reference in the field for years to come".