LinBox is a C++ template library of routines for solution of linear algebra problems including linear system solution, rank, determinant, minimal polynomial, characteristic polynomial, and Smith normal form. Algorithms are provided for matrices with integer entries or entries in a finite field. A number of matrix storage types is provided, especially for blackbox representation of sparse or structured matrix classes.A few algorithms for rational matrices are available. LinBox also uses underlying data structures and algorithms for integer, rational, polynomial, finite fields and rings, as well as dense and sparse matrix formats coming from the Givaro (https://casys.gricad-pages.univ-grenoble-alpes.fr/givaro) and FFLAS-FFPACK (http://linbox-team.github.io/fflas-ffpack) libraries.