1. Preliminaries --
2. Tensor products and compound matrices --
3. Hermitian matrices and majorization --
4. Singular values and unitarily invariant norms --
5. Perturbation of matrices --
6. Nonnegative matrices --
7. Completion of partial matrices --
8. Sign patterns --
9. Miscellaneous topics --
10. Applications of matrices.

Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applications. This presents modern perspectives of matrix theory at the level accessible to graduate students