1. Introduction: Hausdorff dimension

2. Singular value function and invariant sets of maps and dynamical systems

3. Lyapunov dimension of maps

4. Lyapunov dimensions of dynamical systems

5. Analytical estimates of the Lyapunov dimension and its invariance with respect to diffeomorphisms

6. Analytical formulas of exact Lyapunov dimension for well-known dynamical systems

8. Computation of the finite-time Lyapunov exponents and dimension in MATLAB

Conclusions