Preface -- 1 Introduction -- 2 Waveguides. Radiation Principle. Scattering Matrices -- 2.1 Boundary Value Problem in a Cylinder -- 2.2 Problem in a Domain G with Cylindrical Ends -- 2.3 Waves and Scattering Matrices -- 3 Properties of Scattering Matrices in a Vicinity of Thresholds -- 3.1 Augmented Space of Waves -- 3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices -- 3.3 Other Properties of the Scattering Matrices -- 4 Method for Computing Scattering Matrices -- 4.1 A Method for Computing Scattering Matrices outside Thresholds -- 4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds -- 5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy -- 5.1 Statement of the Problem -- 5.2 Limit Problems -- 5.3 Special Solutions to the First Kind Homogeneous Problems -- 5.4 Asymptotic Formulas -- 5.5 Justification of the Asymptotics -- 5.6 Comparison of Asymptotic and Numerical Results -- 5.7 The Impact of a Finite Waveguide Work Function on Resonant Tunneling -- 6 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy -- 6.1 Statement of the Problem and Outline of the Results -- 6.2 Limit Problems -- 6.3 Tunneling in a Waveguide with One Narrow -- 6.4 Tunneling in a Waveguide with Two Narrows -- 7 Resonant Tunneling in 2D Waveguides in Magnetic Field -- 7.1 Statement of the Problem -- 7.2 The Limit Problems -- 7.3 Special Solutions to Homogeneous First Kind Limit Problems -- 7.4 Asymptotic Formulas -- 7.5 Justification of the Asymptotics -- 7.6 Comparison of Asymptotic and Numerical Approaches -- 8 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section -- 8.1 Introduction -- 8.2 Statement of the Problem -- 8.3 Limit Problems -- 8.4 Special Solutions of Limit Problems -- 8.5 Asymptotic Formulas -- 8.6 Justification of the Asymptotics -- 9 Numerical Simulation of High Energy Electron Transport -- 9.1 Numerical Simulation of Multichannel Resonant Tunneling -- 9.2 Fano Resonances.-10 Asymptotic Analysis of Multichannel Resonant Tunneling -- 10.1 Statement of the Problem and Limit problems -- 10.2 Tunneling in a Waveguide with One Narrow -- 10.3 Tunneling in a Waveguide with Two Narrows -- 11 Electronics Devices Based on Resonant Tunneling -- 11.1 Magnetic Field Sensors Based on Quantum Waveguides -- 11.2 Transistors Based on Quantum Waveguides -- 11.3 Electron Flow Switch for Quantum Nets -- Bibliography.