The Basic Linear Algebra Subprograms (BLAS) library is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. Many numerical software applications use BLAS-compatible libraries to do linear algebra computations, including Armadillo, LAPACK, LINPACK, GNU Octave, Mathematica, MATLAB, NumPy, R, and Julia.

This is a list of notable numerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions.