ALGAU, or ALLGAU  , the name now given to a comparatively small district forming the south-western corner of Bavaria, and belonging to the province of Swabia and Neuburg, but formerly applied to a much larger territory, which extended as far as the Danube on the N., the Inn on the S. and the Lech on the W . The Algau Alps contain several lofty peaks, the highest of which is Madelegabel (8681 ft.) . The district is celebrated for its cattle, milk, butter and cheese .