1. In the bowl of an electric mixer fitted with the paddle attachment, dissolve the yeast and sugar in the warm water, and let stand until bubbly, about five minutes.

2. Add 1 cup of the flour, and beat at medium speed until incorporated. Add the eggs, one at a time, then the margarine or oil. Add an additional 1 cup flour, and beat on high speed for 3 minutes.

3. Attach the dough hook, and add the salt and the remaining 3 cups flour. Knead until smooth, about 10 minutes. Alternatively, combine all the ingredients as directed, but beat them together with a wooden spoon. Once they are fully incorporated, turn the dough out onto a lightly floured work surface, and knead until smooth, about 15 minutes.

4. Roll the dough into a ball, and place in an oiled bowl. Turn to coat all surfaces with oil. Cover with a damp kitchen towel or plastic wrap, and let rise in a warm place until doubled in bulk, about 1 1/2 hours.

5. Punch down the dough, and turn it out onto a floured surface. For a single-braid loaf, divide the dough into three equal portions. For two single-braid loaves, divide the dough in half, then divide each half into three equal portions. For a triple-braid loaf, divide the dough into three unequal portions - large, medium and small - then divide each of these portions into three equal portions.

Preheat oven to 350°F.

6. In each case, using your palms, roll out each dough portion on a lightly floured surface into a rope no longer than 12 inches. The size will depend upon which loaf you are making. Braid each set of three ropes, pressing the ends together and tucking them under slightly. If making one or two single-braid loaves, simply place them on an oiled baking sheet once they are formed. If making a triple-braid loaf, place the largest braid on an oiled baking sheet. Lay the medium braid on top and press firmly to attach it. Then, top the littlest braid, again pressing to attach it. Cover the bread(s) with a kitchen towel and let rise until doubled in bulk, about 45 minutes.

7. Just before baking, brush the loaves with the egg, and sprinkle with sesame or poppy seeds. Bake until golden, about 30 minutes for the two small loaves, about 40 minutes for the large single-braid loaf and as long as 50 minutes for the triple-braid loaf. Test for doneness by tapping the bottoms of the loaves; they should sound hollow.

8. Let cool on wire racks. Makes one large or two small loaves.