Phonons are always present in the solid state even at an absolute temperature of 0 K where zero point vibrations still abound. Moreover, phonons interact with all other excitations of the solid state and, thereby, influence most of its properties. Historically experimental information on phonon transport came from measurements of thermal conductivity. Over the past two decades much more, and much more detailed, information on phonon transport and on many of the inherent phonon interaction processes have come to light from experiments which use nonequilibrium phonons to study their dynamics. The resultant research field has most recently blossomed with the development of ever more sophisticated experimental and theoretical methods which can be applied to it. In fact, the field is moving so rapidly that new members of the research community have difficulties in keeping up to date. This NATO Advanced Study Institute (ASI) was organized with the objective of overcoming the information barrier between those expert in the field and those who are new to it. Thus it was decided to (i) organize a set of tutorially based lectures covering most of the important facets in the field, and (ii) to produce an Institute proceedings which would serve both as the first general textbook, as well as a valuable reference book, for this field of knowledge.