The se are the proceedings of the colloquium on potential theory held in Copenhagen, May 14th - 18th, 1979, on the occasion of the 500th anniver- sary 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. Ørsted Inst itute. 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 proceed ings).