Among vegetarians there are a number of subsets, including some (vegans) who use no dairy products or eggs, and some who use dairy products but no eggs. And, of course, a great many people are allergic to eggs or avoid them because of the cholesterol.

Tofu is a good replacement for eggs in many dishes like quiche, lasagna or cannelloni. Any number of tofu cookbooks on the market today can help you learn how to substitute them.

Then there are "egg replacers," commercial products made of refined starches, modified vegetable gums and leavening. They go a fair distance toward matching the binding power of eggs. Most health food stores offer these products -- Mariclare Barrett of Vegetarian Times suggests a home version: 1 tablespoon arrowroot, 1 tablespoon soy flour and 2 tablespoons of water is a substitute for one egg and will bind most standard cake and quick-bread recipes. For making vegetable patties and burgers, grated cooked potato can help bind ingredients together.

On the whole, cooking without eggs is not difficult; the most challenging area is cakes and cookies. From the January issue of Vegetarian Times comes a recipe for eggless vanilla cake that is one of the very best I've tried. Be sure to let it cool thoroughly before you take it out of the pan. This one layers nicely.

Our pattern-cookie recipe is great for making gingerbread people and animal shapes. It, too, is eggless.

PETER'S VANILLA CAKE (6 to 8 servings)

1 3/4 cups whole-wheat pastry flour

1 teaspoon baking powder

1/2 teaspoon salt

3/4 cup maple syrup

1/3 cup safflower oil

2/3 cup water

2 teaspoons vanilla extract

1 tablespoon apple cider vinegar

Sift dry ingredients in a mixing bowl. Whip together liquid ingredients. Pour liquid ingredients into dry. Stir with a wooden spoon until smooth, with no lumps remaining. Pour batter into an oiled, 9-inch cake pan. Bake in a 375-degree oven for 30 to 40 minutes or until a toothpick comes out dry.

Allow to cool for a few minutes, then remove from pan. Let cake cook before frosting.

SPICY PATTERN COOKIES (Makes 4 dozen 2-inch cookies)

1/4 cup ( 1/2 stick) butter

1/4 cup brown sugar

1/2 cup dark molasses

3 cups whole-wheat flour

1 teaspoon baking soda

1/2 teaspoon salt

1 teaspoon ginger

1/2 teaspoon cinnamon

1/4 teaspoon cloves

1/2 cup wheat germ

1/2 cup water, approximately

Cream butter and sugar and beat in the molasses. Sift the flour, setting aside any bran that remains behind to add later. Sift again with the soda, salt and spices, then stir in wheat germ and reserved bran. Mix dry ingredients into molasses mixture, adding enough of the water to make a workable dough.

Roll dough out about 1/4-thick (thinner if you prefer), and cut into shapes. Transfer to greased cookie sheets and bake for about 10 minutes at 350 degrees, until just barely beginning to brown.

Decorate by pressing in currants, filbert halves, etc. before baking, or with a simple confectioners' sugar frosting after the cookies have cooled.