Pt. I. Solvable Systems. 1. Review of Solvable Systems -- Pt. II. The Geometry of Mechanics. 2. Geometry of Mechanics I: Linear. 3. Geometry of Mechanics II: Curvilinear. 4. Geometry of Mechanics III: Multilinear -- Pt. III. Lagrangian Mechanics. 5. Lagrange -- Poincare Description of Mechanics. 6. Simplifying the Poincare Equation With Group Theory. 7. Conservation Laws and Symmetry -- Pt. IV. Newtonian Mechanics. 8. Gauge-Invariant Mechanics. 9. Geometric Phases -- Pt. V. Hamiltonian Mechanics. 10. Hamiltonian Treatment of Geometric Optics. 11. Hamilton -- Jacobi Theory. 12. Relativistic Mechanics. 13. Symplectic Mechanics -- Pt. VI. Approximate Methods. 14. Analytic Basis for Approximation. 15. Linear Systems. 16. Perturbation Theory.