Scrub the beets free of dirt and soil. Put them in a pot and pour water over them until they are covered. Boil the beets for about 60 minutes in lightly salted water. Pour cold tap water over them and let them cool off. Cooling in cold water makes it much easier to "peel" the skin off the beets. Cut the top and bottom off the cooked beets and "slip" or "peel" them out of their skin. Slice the beets into thin slices of 2-3 millimeters. Place the beet slices in sterilized canning jars. Do not fill the jars completely, as there should be room for the brine. Put all the ingredients for the pickling brine in a pot and bring it to a boil. Boil the brine until the sugar has melted. Pour the hot brine over the beets and seal the jars. Store the pickled beets in a cool place.