In recent years, Hamilton-Jacobi equations have attracted a lot of attention due to the important role that they play in various fields of applications.In this book, we introduce recent developments in adaptive numerical methods for Hamilton-Jacobi equations.We construct convergent adaptive high order schemes for time dependent Hamilton-Jacobi equations and propose a general method of constructing convergent adapive high order schemes and discuss the question of its convergence.Then, we propose a method of constructing convergent adaptive high order schemes for Hamilton-Jacobi equations on...