This chapter contains the basic results of Hermitian matrices and the techniques used to derive the results. Sect. 8.1 presents equivalent conditions of matrices being Hermitian, Sect. 8.2 gives some trace inequalities and discusses a necessary and sufficient condition for a square matrix to be a product of two Hermitian matrices, and Sect. 8.3 develops the min-max theorem (principle) and the interlacing theorem for eigenvalues. Sect. 8.4 gives some simple eigenvalue and singular value inequalities of Hermitian matrices, Sect. 8.5 shows a few advanced eigenvalue inequalities of the sum of Hermitian matrices by min-max expressions, and Sect. 8.6 presents a matrix version of the triangle inequality.