This book describes new, highly effective, rigorous analysis methods for electromagnetic wave problems. Examples of their application to the mathematical modelling of micros trip lines, corrugated flexible waveguides, horn antennas, complex-shaped cavity resonators and periodic structures are considered. Special attention is paid to energy dissipation effects. Various physical models and methods of analysis of dissipation are described and approximate formulas and computer-based calculation results for dissipation characteristics are given and compared with experimental data. Ways of decreasing dissipation in waveguides and resonators are discussed. The book will be of interest to physicists and engineers working on the theory and design of microwave and millimetre-wave components and devices. Designers in microwave engineering will find here all the information they need for choosing the correct waveguide (resonator) for a stipulated dissipation characteristic. The numerical algorithms and formulas can be directly applied to CAD systems. The book is also relevant for students of electromagnetism and microwave circuits.