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Recent advances in our understanding of complex composite media, especially chiral media for microwave applications, suggest the feasibility of creating novel materials with unusual properties and the possibility of constructing new microwave devices using such materials. The emphasis of the book is on bi-anisotropic materials, whose most interesting feature is the magnetoelectric interaction of the fields. The materials are expected to supply useful applications in radar technology, aerospace, microwave engineering, manufacturing technology, etc., such as absorbers for low-reflectivity shields, reciprocal phase shifters, polarization transformers. The first experiments with artificial bi-anisotropic media have been successfully carried out.I. General.- Fedorovs Covariant Methods in the Electromagnetic Field Theory.- Developments of Fedorov Covariant Methods and Applications to Optically Active Crystals.- Bi-Isotropic and Bi-Anisotropic Media (General Review).- II. Fundamental Issues of Bi-Anisotropic Electromagnetics.- Covariant Multipole D and H Fields for Reflection from a Magnetic An isotropic Chiral Medium.- Jones Transmission and Reflection Matrices for Low-Symmetric Absorbing Gyrotropic Crystals.- Inverse Problem of Reflection and Transmission for a Bianisotropic Medium.- Chiral Effects and Eigenwaves in Bi-Anisotropic Omega Structures.- Pulse Distortion by a Lossy, Resonant Chiral Medium.- III. Continuum Modelling of Complex Media.- Non-Local Response of Composite Materials in Microwave Range.- Effective-Medium Theories for Bi-Isotropic Mixtures.- Effective Material Parameters of Plane Stratified Bianisotropic Superlattices.- Weakly Nonlinear Chiral Composites: the Bruggeman and the Maxwell Garnett Models.- Optically Induced Rotating Spatially Uniform Structure in Chiral Media.- Faraday Effect and Magnetogyration in Superlattices in the Long Wave length Approximation.- IV. Scattering and Diffraction from Bi-Anisotropic Structures.- Electromagnetil`