Introduction and Overview; Review of Basic Concepts and Results from Theoretical Linear Algebra; Fundamental Tools and Concepts from Numerical Linear Algebra; Canonical Forms Obtained via Orthogonal Transformations; Linear State Space Models and Solutions of the State Equations; Contollability, Observability and Distance to Uncontrollability; Stability, Inertia and Robust Stability; Numerical Solutions and Conditioning of Lyapunov and Sylvester Equations; Realization and Subspace Identification; Feedback Stabilization, Eigenvalue Assignment and Optimal Control; Numerical Methods and Conditioning of the Eigenvalue Assignment Problems; State Estimation; Numerical Solutions and Conditioning of Algebraic Riccati Equations; Internal Balancing and Model Reduction; Large-Scale Matrix Computations in Control: Krylov Subspace Methods; Numerical Methods for Matrix-Second-Order Control Systems; Existing Software for Control Systems Design and Analysis