Wave propagation is any of the ways in which waves travel. With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves. For electromagnetic waves, propagation may occur in a vacuum as well as in a material medium. Other wave types cannot propagate through a vacuum and need a transmission medium to exist. In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. Wave Propagation in Materials and Structures is devoted to the modern methods developed to describe wave propagation in modern materials and structures. The book contains original works of prominent scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. Elastic wave propagation has been used for years for assessment of the structural integrity of engineering materials. The advantage it deals is the direct association to elastic properties, the quite easy application through commercial equipment along with numerous empirical correlations between pulse velocity and material strength or quality in general. Advanced features like frequency dependence of wave parameters may further improve the characterisation capacity. Concrete materials because of their intrinsic microstructure, which is enhanced by the existence of damage-induced cracking, demonstrate a complicated behavior relating to the propagation of pulses of different frequencies. The different wave lengths interact with inhomogeneities according to their size and therefore, leave their signature on the phase velocity and attenuation versus frequency curves. Although experimental measurements are troublesome in concrete structures, mainly due to attenuation of high frequencies, it is suggested that, whenever possible, application of different frequencies can provide a more detailed insight on the internal condition of the structure. This book intends to basic and advanced concepts of wave propagation in diverse material systems and structures. Such a text is necessary considering the multi-disciplinary nature of the subject. Therefore, actively working readers (scientists, engineers, students, as well as researchers and practitioners) will find many interesting results and new ideas in this book.