Trim beets, leaving 1 inch of stem attached. Place beets in large pot, cover with water and bring to a boil. Reduce heat and simmer for 25 to 40 minutes or until tender. Drain and rinse under cold water. Remove skins and cut beats into serving sized pieces.

Combine vinegar, sugar, and water in saucepan. Bring to boil, stirring occasionally.

Into sterilized jars divide shallots, caraway seeds, and mustard seeds equally among jars. Add beets pieces.

Pour boiling vinegar mixture over beets to within 1/2 inch of rim. Process in water bath for 30 minutes for 500mL jars and 35 minutes for 1L jars.