The purpose of the course is to impart in-depth theoretical knowledge and innovative methodological approaches to the participants in the study of the phenomena associated with the propagation of mechanical waves in deformable solids for the solution of relevant problems in structural and geotechnical engineering, seismology and applied geophysics. The course is addressed to scholars with different background however sharing a common interest in the subject of propagation of vibratory waves in deformable continua of different nature including soils, rocks and construction materials. It is expected that at the end of the course, the attendees will have mastered the tools of analysis introduced to them so as to be able to independently investigate research topics of interest not covered in class.