This volume (Parts A and B) contains the edited papers presented at the annual Review of Progress in Quantitative Nondestructive Evaluation held at the University of California - San Diego, La Jolla, CA, on August 1-5, 1988. The Review was organized by the Center for NDE at Iowa State University and the Ames Laboratory of the U. S. Department of Energy in cooperation with the Air Force Materials Laboratory, the Office of Basic Energy Sciences, USDOE, the Office of Naval Research, the NASA-Langley Research Center, and The Metallurgical Society (TMS). Yith a total of over 450 participants from the US and nine foreign countries who presented a record 325 papers, this conference has grown into the largest, most significant gathering of NDE researchers and engineers anywhere in the Yest. The meeting was divided into 36 sessions with as many as four sessions running concurrently. All stages of NDE development from basic research investigations to early engineering applications and all methods of inspection science from ultrasonics to x-ray tomography were covered. Following a pattern now familiar to regular attendees of the Review and readers of the Proceedings, the editors have organized the papers in the Proceedings according to topical subject headings rather than the original order of presentation. This rearrangement yields a more user friendly reference work. Part A of the Proceedings treats NDE technique development whereas Part B is organized around the theme of materials.