The ITPACK project: Past, present, and future The ITPACK project at The University of Texas at Austin involves the development of research-oriented mathematical software, based on iterative algorithms, for solving large systems of linear algebraic equations with sparse coefficient matrices. The emphasis is on linear systems arising in the solution of partial differential equations by discretizations such as finite difference or finite element methods. Among other things this project has resulted in the development of a computer package of subroutines known as ITPACK 2C which is available to the scientific community. Features of the ITPACK routines include the adaptive determination of the iteration parameters and realistic procedures for terminating the iterative processes. An important application of ITPACK 2C is for use as solution modules in the ELLPACK package of computer routines for solving a class of elliptic partial differential equations. par This paper reviews the objectives of the ITPACK project, summarizes the programs made to date and outlines plans for future work. A summary is given of work on both software and research that has contributed to the present mathematical software package. The 2C version of ITPACK for scalar computers and a version for use on high performance vector computers are discussed. An overview is given of the development work on other software involving more general preconditioners and additional nonsymmetric procedures.