INN, a river of Europe, one of the principal affluents of the Danube. It rises in a lake in the southern part of the Swiss canton of Les Grisons, and follows a N.E. course until it falls into the Danube at Passau. It flows through the deep and narrow valley of the Engadine, through Tyrol and Bavaria, and latterly forms the boundary between Bavaria and Austria. Its length is about 250 miles.