Tutorial Information Today, a desktop computer with a multicore processor and a GPU accelerator can already provide a teraFLOPS of performance. This tremendous computational power can only be fully utilized with the appropriate software infrastructure. Most often a major part of the computational effort in scientific and engineering computing goes towards solving linear algebra sub-problems. This tutorial surveys the state-of-the-art numerical libraries for solving problems in dense and sparse linear algebra. The tutorial consists of three parts. The first part provides a brief historical look at the development of dense linear algebra libraries, from LINPACK, to LAPACK, to ScaLAPACK. The second part discusses dense linear algebra software for multicore processors (PLASMA) and hardware accelerators (MAGMA). The fourth part will presents software for sparse liner algebra, including the Trilinos package.