This chapter Presents the essential mathematical tools—linear algebra and probability—that form the backbone of quantum computation. Previous knowledge of elementary linear algebra is assumed. Dirac notation is adopted from the onset, and Pauli Matrices are introduced. Concepts relevant to this Book, including matrix norms, condition number, projection matrices, Hermitian matrices, unitary matrices, the eigenvalue decomposition, the singular value decomposition, and the Krylov subspace are presented with their key properties. The two Major classes of inear Ssystem solvers—direct and iterative solvers—are briefly introduced with a discussion of their asymptotic caling. The chapter concludes with an introduction to Kronecker products and their properties.