Linear algebra is fundamental to many scientific computing applications. It is therefore crucial to have high-quality linear algebra libraries that are optimized for specific hardware architectures. In this chapter, we discuss the de facto standard for implementing basic vector and matrix operations, BLAS, and the high-quality implementation of linear algebra routines, LAPACK. LAPACK leverages the BLAS to provide optimized routines for solving linear algebra problems. We also discuss the FFTW library, which provides optimized routines for computing discrete Fourier transforms (DFT). Discrete Fourier transforms are another common operation in scientific computing applications that are often expensive to compute.