NUCLEI, CHAOS AND STATISTICAL SPECTROSCOPY Kamales Kar Saha Institute of Nuclear Physics Calcutta, India ABSTRACT The talk in the first part will review the application of random matrix theory to nuclear spectra and their fluctuations as well as the well-known connection to chaos in quantum many-body systems. The extension of GOE, called 'Embedded GOE' or EGOE is found suitable to describe nuclei and results for average nuclear properties in this ensemble will be presented. Averaged forms for occupacies, strengths and strength sums of nuclear transition operators can also be obtained and compared with detailed shell model results to demonstrate their usefulness.