The Parma Polyhedra Library (PPL) is a modern C++ library providing numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems. The PPL can handle all the convex polyhedra that can be defined as the intersection of a finite number of (open or closed) hyperspaces, each described by an equality or inequality (strict or non-strict) with rational coefficients. The PPL also supports finite powersets and products of (any kind of) polyhedra and grids, a mixed integer linear programming problem solver using an exact-arithmetic version of the simplex algorithm, a parametric integer programming solver, and primitives for termination analysis via the automatic synthesis of linear ranking functions.