Intro
Preface
Acknowledgements
Contents
About the Authors
Part I Toric Geometry and Logarithmic Curve Counting
1 Enumerative Geometry
2 The Tropical Approach
3 Our Guiding Problem
4 Compactifying the Problem
5 Calculation via Combinatorics
1 Geometry of Toric Varieties
1.1 Basics
1.2 The Dual Side
1.3 The Toric Dictionary
1.4 A Few Toric Exercises
2 Compactifying Subvarieties of Tori
2.1 Compactifying Subvarieties of Tori
2.2 Tropicalization via Compactifications
2.3 Tropicalizations via Valuations
2.4 Varying the Coefficients

6.6 Exercises
7 Tropical Hurwitz Theory
7.1 Double Hurwitz Numbers
7.2 Tropical Double Hurwitz Numbers
7.3 Correspondence by Cut and Join
7.4 Correspondence by Degeneration Formula
7.5 Tropical General Hurwitz Numbers
7.6 Conjectural ELSV for Double Hurwitz numbers
7.7 Exercises
8 Hurwitz Numbers from Piecewise Polynomials
8.1 Double Hurwitz Numbers Through DR
8.2 Double Hurwitz Numbers as Boundary Intersections
8.2.1 Lower genus Double Hurwitz Numbers and DRg(x,0)
8.3 Leaky Hurwitz Numbers
8.4 Exercises
Part III Tropical Plane Curve Counting

9 Introduction to Plane Tropical Curve Counts
9.1 Tropical Polynomials
9.2 Tropical Hypersurfaces and Duality
9.3 Degenerations of Algebraic Curves and Kapranov's Theorem
9.4 Parametrizing Tropical Plane Curves
9.5 The Correspondence Theorem
9.6 Exercises
10 Lattice Paths and the Caporaso-Harris Formula
10.1 Lattice Paths
10.2 The Caporaso-Harris Formula
10.3 Generalized Lattice Paths
10.4 Exercises
11 The Caporaso-Harris Formula for Tropical Plane Curves and Floor Diagrams
11.1 The Caporaso-Harris Formula for Tropical Plane Curves
11.2 Floor Diagrams