Alliums -- onions, garlic, chives, leeks, shallots, and green onions -- make up one of the most important culinary plant families. There are more than 300 species of alliums, and many of these have, at one time or other, been used in cooking. Yet we often take members of the allium family for granted. We value their flavors but overlook them as noble ingredients in their own right. Onions are about as omnipresent in cooking as salt. And garlic -- well, imagine pesto, aioli, or hummus without it. All of the alliums featured in this Cooking Class can and do take center stage. Here's a look at the six most popular alliums, listed in order of potency.

GARLIC (allium sativum)

Garlic is the most pungent of all alliums, and the more it is chopped, the stronger it tastes. For subtle garlic flavor, add whole unpeeled cloves to pot roasts and roasted vegetable dishes like Garlic-Roasted Potatoes and Fennel. Asian stir-fries use sliced garlic, which adds warm, toasty flavor. Finely chopped and crushed garlic add strong, "hot" flavor, especially when uncooked.

There are many types of garlic, some purple-skinned, others pearly white. Some produce huge, fat cloves with more subtle flavor than smaller-cloved garlics. So-called "elephant" garlics, with huge, mild-tasting bulbs as long as three inches, are related to the wild leek (allium ampeloprasum). Young, or green, garlic is a mild seasonal treat that usually arrives in markets in early summer. Both young garlic and elephant garlic can be baked whole in foil then squeezed out of their skins to yield a deeply flavored puree that's good in pasta sauces and dips, with goat cheeses, or spread on toasted sourdough. Garlic stores well -- you can keep it hung on a rope or braid in a cool place for several months.

ONIONS (allium cepa)

This allium's bulb keeps it alive during dormancy. As onions age, they become sweeter and milder. Red onions and sweet onions, including Vidalia, Walla Walla, Oso, and Yellow Bermuda, contain more sugars than brown- or white-skinned Spanish varieties. Freshly harvested onions of any variety have a much stronger taste than stored onions.

Onions are the workhorses of the allium family, yet some varieties are more suitable for specific uses than others. Sweet onions are great raw in salads and for making quick pickles. Hotter brown- and white-skinned onions are best for soups and stews, and for baking or roasting whole or in wedges. Red onions cook to an unappetizing grayish brown, so use them only in salads or quick-cook dishes that allow them to maintain their glorious color. Small onions are useful for cooking whole in stews and ragouts, and for pickling. Cipollini onions are small and pale yellow, and their flatness allows them to cook quickly and evenly.SHALLOTS (allium cepa varieties)

Shallots differ from onions in that many varieties produce a cluster of several bulbs to a plant. Shallots also have finer layers and less water. Because of the low water content, their flavor is more concentrated than that of onions, but they can also burn and toughen easily, so use caution when sautéing.

Use shallots when you want full allium flavor but not the bulk of a full-sized onion. Traditionally, shallots are used to flavor the reductions in some French sauces, including bearnaise bordelaise, and duxelles. Shallots are also delicious cooked whole -- try them caramelized with sugar and a few tablespoons of cognac, port, or sherry, or oven-roasted with rosemary or thyme. Finely chopped shallots are good in salad dressings and as a classic accompaniment to fresh oysters or beef dishes.

LEEKS (allium ampeloprasum or allium porrum)

Although leeks resemble large green onions, they're milder and sweeter, and they don't cause any tears when they're chopped.

Unlike other alliums, leeks are almost always enjoyed cooked since they're very fibrous when raw. The tougher, green part usually has a coarser flavor than the white part. Use the green part to flavor soups and stocks; add the white part (which is tender and needs only brief cooking) to soups and stews toward the end of cooking.

Leek soups rank among the world's favorites: from vichyssoise, created by Chef Louis Diat at New York's Ritz-Carlton almost a century ago, to the more provincial potage bonne femme, a creamy vegetable soup. Leeks are also delicious in potato, rice, and pasta dishes, such as Pasta with Leek, Pepper, and Chive Sauce. In some markets you may find finger-slim "baby" or "miniature" leeks. These are great for cooking whole; try them grilled with an herb salsa or vegetable dip, or in a tomato sauce or red wine reduction that includes Greek flavors like coriander, bay, and oregano.

GREEN ONIONS (allium cepa varieties and allium fistulosum)

These are also known as scallions, spring onions, or salad onions. They derive from several different types of wild alliums. And they can vary in thickness and length. Choose slender green onions for stir-fries or chopping into salsas and salads; cook the thicker ones whole, or add them sliced to dishes that cook quickly. Look for red spring onions in farmers' markets -- they add flavor and color to salads.

Served raw, green onions have a sweet, delicate flavor that is excellent in potato or rice salads and in salsas with chiles. Cooked green onions are great for fast recipes such as pasta, omelettes, pancakes, and stir-fries. In Catalonia, in northeastern Spain, green onions known as calcots are grilled over charcoal and served with a chili, garlic, and hazelnut romesco sauce.

CHIVES (allium schoenoprasum)

Chives are among the mildest culinary alliums. We use them primarily as an herb or garnish, but their subtle onion flavor can add just the right note of freshness to an otherwise lackluster dish. Chives are especially delicious with potatoes, eggs, rice, and smoked or pickled fish. The edible lilac-pink flowers of homegrown chives are attractive scattered over salads or omelettes. If you cook with chives, keep it brief to preserve their flavor.

Chives vary from grass-fine to pencil-thick. The thicker the chive, the more flavor it packs.

In Asian markets you may find Chinese or Asian chives (allium tuberosum), also known as ku chai, gow choy, or garlic chives. They have a definite garlic kick; try them stir-fried with chicken or whitefish, or cook them with rice. Always use chives fresh: Dried chives lack the bright flavor that is the key to their charm.