Nondestructive evaluation (NDE) procedures are needed for materials processing, as well as for post-process materials testing. They play important roles in product design, analysis of service-life expectancy, manufacturing and quality control of manufactured products. They are also essential to on-line monitoring of the integrity of structural elements and complex systems. Rational accept and reject criteria should be based on NDE tests. Critical safety, efficiency and operational features of large-scale structures depend on adequate NDE capabilities. The lectures presented in this volume are concerned with quantitative ultrasonic NDE. They present fundamental concepts and basic theory, as well as applications to the detection of cracks and the evaluation of material properties. The following topics are discussed: basic wave propagation theory for ultrasonic NDE; piezoelectric transducers, EMATS and ultrasonic spectroscopy; laser-based ultrasonics; acoustoelasticity; ultrasound in solids with porosity, microcracking and polycrystalline structuring; the determination of mechanical properties of composite materials; inverse problems and imaging.