Scope of the course is to provide in-depth theoretical knowledge and innovative methodological approaches in the study of the phenomena associated with the propagation of mechanical waves in deformable solids. The course is addressed to scholars working in different, yet interacting research fields including structural mechanics, geophysics, seismology and geotechnical engineering. Thus, it is a cross-domain course intended to bridge the gaps among the above disciplines when studying the propagation of mechanical disturbances in natural (e.g. soils, rocks) and construction materials (e.g., steel, concrete). Although the emphasis of the course is on mathematical and constitutive modeling, an effort is made by the instructor to illustrate applications of the theories to the solution of problems taken from real-world situations. It is expected that at the end of the course the participants will have mastered the tools of analysis introduced to them so to independently investigate their research topics.