This report contains the edited transcripts of the Review of Progress in Quantitative Nondestructive Evaluation held at the Scripps Institution of Oceanography, July 14-18, 1980. The review was sponsored by the Defense Advanced Research Projects Agency and the Materials Laboratory of the Air Force Wright Aeronautical Laboratories as a part of the Interdisciplinary Program for Quantitative NDE, Contract No. F33615-80-C-5004. Arrangements for the Review were made by the Science Center, Rockwell International, host organization for the Interdisciplinary Program, and the Scripps Institution of Oceanography, Dr. William A. Nierenberg, Director.