LaGriT is a library of user callable tools that provide mesh generation, mesh optimization and dynamic mesh maintenance in three dimensions for a variety of applications. Geometric regions within arbitrarily complicated geometries are defined as combinations of bounding surfaces, where the surfaces are described analytically or as collections of points in space. A variety of techniques for distributing points within these geometric regions are provided. Mesh generation uses a Delaunay tetrahedralization algorithm that respects material interfaces and assures that there are no internal negative coupling coefficients. The data structures created to implement this algorithm are compact and powerful and expandable to include hybrid meshes as well as tetrahedral meshes. Mesh refinement and smoothing are available to modify the mesh to provide more resolution in areas of interest. Mesh refinement adds nodes to the mesh based on geometric criteria such as edge length or based on field variable criteria such change in field. Mesh smoothing moves nodes to adapt the mesh to field variable measures, and, at the same time, maintains quality element shape. Mesh elements may become distorted as mesh nodes move during a time dependent simulation or are added as a result of refinement operations. Mesh reconnection via a series of edge flips will maintain the Delaunay criterion of the mesh. An additional requirement of time dependent simulations is that as interface surfaces move, the corresponding region definitions must respond dynamically. As surfaces collide, the mesh must respond by merging points and effectively squeezing out the material between the colliding surfaces. LaGriT provides the necessary tools for time dependent simulations.