Ch. I. Equations and problems of narrow beam mechanics -- Ch. II. Hamiltonian formalism of narrow beams -- Ch. III. Approximate solutions of the nonstationary transport equation -- Ch. IV. Stationary Hamilton-Jacobi and transport equations -- Ch. V. Complex Hamiltonian formalism of compact (cyclic) beams -- Ch. VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics -- Appendix A: Complex germ generated by a linear connection -- Appendix B: Asymptotic solutions with pure imaginary phase and the tunnel equation -- Appendix C: Analytic asymptotics of oscillatory decreasing type (heuristic considerations).