1 Introduction
1.1 The atmospheric boundary layer
1.2 Waveguides
1.2.1 Evaporation duct
1.2.2 Elevated M-inversion, tropospheric duct
1.3 Turbulent fluctuations of the refractive index

2 Mathematical methods for UHF wave propagation and scattering in the troposphere
2.1 Parabolic approximation to a wave equation for spherically stratified media filled with turbulent irregularities of the refractive index.
2.2 Green's function for a parabolic equation in a stratified troposphere
2.3 Feynman path integral for wave propagation in random media

3 Wave field fluctuations in random media over a boundary interface
3.1 Reflection formulas for the wave field in random media over an ideally reflective boundary
3.2 Wave field fluctuations over the surface with impedance boundary conditions

4 Radio wave propagation in the evaporation duct
4.1 Perturbation theory for the spectrum of normal waves in a non-uniform troposphere
4.2 Spectrum of the normal waves in evaporation duct
4.3 Coherence function of the wave field in a random non-uniform troposphere
4.4 Excitation of the wave of continuous spectrum in a evaporation duct with random inhomogeneities of the refractive index

5 Impact of elevated M-inversions on the UHF/EHF field propagation beyond the horizon
5.1 Spectrum of the normal waves for the wave field in the presence of elevated M-inversion
5.2 Interaction between evaporation duct and elevated M-inversion
5.3 Excitation of the normal waves in elevated duct due to a wave scattering on random inhomogeneities of the refractive index

6 Non-conventional propagation mechanisms
6.1 Impact from random stratification of the refractive index on the UHF signal level over horizon
6.2 Single-scattering theory of the diffracted field

7 Appendix: Airy Functions