1. In a medium or large pot, boil beet, potatoes and carrots (for about 30-40minutes). Let them cool till room temperature.
2. Hard boil the eggs (after bringing water to a rapid boil, cook for an additional 10 minutes). When the eggs are ready, chill them by placing under cold running water for a few minutes.
3. Peel the eggs and separate whites from yolks. Grate whites and yolks separately.
4. Using large holes of a box grater, grate separately the potatoes, beet and carrot.
5. Finely chop the onion.
6. Dice the herring fillets into small chunks.
7. Take a large plate and form an even round layer of grated potatoes in the middle of the plate. Put a thin layer of mayonnaise on top of the potatoes. To squirt mayonnaise, use a pastry bag or a plastic sandwich bag (cut a small hole at one corner of the plastic bag so the mayonnaise can pass through). You can also spread mayonnaise using a spatula.
8. Add the herring as the second layer, and a thin layer of mayonnaise on top of it.
9. Place the onion and carrot on top of the herring layer and spread mayonnaise on them.
10. Cover the salad with a layer of beet.
11. Add a layer of mayonnaise. Decorate the salad with grated egg whites and yolks.
12. Let cool in refrigerator for at least 1 hour. Use a knife to cut into segments. Serve.