These are the proceedings of the colloquium on potential theory held in Copenhagen, May 14th - 18th, 1979, on the occasion of the 500th
anniversary of the University of Copenhagen. The colloquium was sponsored by the Danish-French Society for Scientific Research and Exchange, and took place at the H. C. 0rsted Institute. There were 71 participants from 18 countries. The scientific programme comprised 44 lectures and a "Table
ronde", where open problems were discussed (cf. the problem section at the end of these proceedings).