The Software for Linear Algebra Targeting Exascale (SLATE) provides fundamental dense linear algebra capabilities to the high-performance computing (HPC) community.SLATE provides basic dense matrix operations (e.g., matrix multiplication, rank-k update, triangular solve), linear systems solvers, least square solvers, singular value and eigenvalue solvers.The ultimate objective of SLATE is to replace the venerable Scalable Linear Algebra PACKage (ScaLAPACK) library, which has become the industry standard for dense linear algebra operations in distributed memory environments. However, after two decades of operation, ScaLAPACK is past the end of its lifecycle and overdue for a replacement, as it can hardly be retrofitted to support hardware accelerators, which are an integral part of today’s HPC hardware infrastructure.Primarily, SLATE aims to extract the full performance potential and maximum scalability from modern, many-node HPC machines with large numbers of cores and multiple hardware accelerators per node. For typical dense linear algebra workloads, this means getting close to the theoretical peak performance and scaling to the full size of the machine (i.e., thousands to tens of thousands of nodes). This is to be accomplished in a portable manner by relying on standards like MPI and OpenMP.SLATE functionalities will first be delivered to the ECP applications that most urgently require SLATE capabilities (e.g., EXascale Atomistics with Accuracy, Length, and Time [EXAALT], NorthWest computational Chemistry for Exascale [NWChemEx], Quantum Monte Carlo PACKage [QMCPACK], General Atomic and Molecular Electronic Structure System [GAMESS], CANcer Distributed Learning Environment [CANDLE]) and to other software libraries that rely on underlying dense linear algebra services (e.g., Factorization Based Sparse Solvers and Preconditioners [FBSS]). SLATE will also fill the void left by ScaLAPACK’s inability to utilize hardware accelerators, and it will ease the difficulties associated with ScaLAPACK’s legacy matrix layout and Fortran API.