Title: Double beta decay theory, in particular an ``anatomy" of the 
        nuclear matrix elements.

Abstract: There are three sets of issues to consider. First, a 
problem of the mechanism. If the decay is observed, how can we tell 
whether it is caused by the virtual exchange of a light Majorana 
neutrino between the participating nucleons, or by the exchange of 
some other, TeV mass, particle? Then there are issues related to 
nucleon structure, nucleon form factors, induced currents and 
short range correlations. And finally, the most important set, 
understanding nuclear structure of the ground states of 
participating nuclei. I will touch on all three of these 
sets, with emphasis on the third one.