Schloss Hartenfels is Torgau's great set piece: a large early Renaissance castle rising above the Elbe. It was the residence of the Ernestine electors of Saxony and still has the scale of a court that once mattered.
Look for the grand spiral stair in the courtyard and the castle chapel beside it. The castle is also the best place to start because it explains why Torgau mattered long before it became a quiet provincial town.