Intended mainly for use as a reference manual, this third edition encompasses all the improvements of the newest version of the PLTMG software package, including the following:* The data structures defining the domain (triangulation and skeleton) have been simplified; more general boundary conditions are allowed.* The internal data structure (triangle tree) has been replaced by a simple triangulation; the adaptive algorithms have been revised to use this simple data structure.* The linear equations solvers are multigraph methods, which are simple ILU factorizations with strong connections to the hierarchical basis multigrid method.* The graphics packages have been improved and now include expanded options.* The test driver has a new X-Windows gui option.