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The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems: - comprehensive review of the most popular theories of plates and shells, - relations between three-dimensional theories and two-dimensional ones, - presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories), - modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc., - applications in modeling of non-classical objects like, for example, nanostructures, - presentation of actual numerical tools based on the finite element approach.