Chop cabbage into small pieces. Loosely pack cabbage into 1 quart jars. Don't fill the jar completely; leave about 1-inch from the top of each jar free.
Add 2 tablespoons canning and pickling salt and 2 tablespoons vinegar to each jar. Fill the jars with water leaving about ½-inch from the top free.
Place lids and rings on jars; slightly tighten the rings (should be loose). The fermenting cabbage will cause the jars to expand and seal in about 10-12 days. Place the jars on newspaper in a cool dark place. Let stand 2-3 weeks before eating.