MINOS is a Fortran system for solving large-scale linearly constrained optimization problems. The System Manual gives an overview of the system, the programming conventions used, data structures, tolerances, and error conditions. details are given of a practical implementation for maintaining a sparse LU factorization. The reduced-gradient approach for handling a nonlinear objective function has been described elsewhere; further implementation details are included here. The System Manual should facilitate interfacing of MINOS with other optimization software.