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The book is concerned with new approaches in the transfer matrix method when adopted for the assessment of actual problems in structural engineering. Specified are the properties of new transfer matrices, advanced approaches and techniques for their obtaining as well as the principles of vectorized FETM-approaches. Presented are the new applications for the problems of wave dynamics of advanced composite wood vs carbon fiber structures as well as for the aeroelasticity of slender free sky telescopes and of ultimate behaviour of small channel slabs adopted in present high speed railway engineering, taking into account the comparison with experimental results. The efficiency of the approaches suggested is verified and discussed.