This report contains the edited transcripts of the Review of Progress in Quantitative NDE held at the Scripps Institution of Oceanography, July 8-13, 1979. The Review was sponsored by the Advanced Research Projects Agency and the Air Force Materials Laboratory as a part of the Interdisciplinary Program for Quantitative Flaw Definition, Contract No. F33615-74-C-5180. 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.