I. Equations and problems of narrow beam mechanics -- II. Hamiltonian formalism of narrow beams -- III. Approximate solutions of the nonstationary transport equation -- IV. Stationary Hamilton-Jacobi and transport equations -- V. Complex Hamiltonian formalism of compact (cyclic) beams -- VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics -- References -- 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).