There are 5 Mother Sauces that are prepared in French Cooking:
Béchamel
Queen of all Sauces
Velouté
Not a Finished Sauce
Espagnole
Rich Dark Sauce
Tomato Sauce
Pasta Sauce
Hollandaise
Egg Yolk and Butter sauce
If you’ve eaten homemade macaroni and cheese, moussaka, or lasagna, chances are you’ve experienced the rich creaminess of Béchamel. It can be made in its most basic form by just combining roux and milk, or it can be mixed with other ingredients to create new sauces: Mornay is made by adding Gruyère or Parmesan, and mustard sauce is made by adding—you guessed it—mustard. A simpler version is the white pan sauce.
Like good old Béchamel, Velouté begins with a white roux, but then it gets mixed with white stock made from fish, chicken, or veal. Technically not a finished sauce, it's used as a flavorful starting point for gravies, mushroom sauces (pot pie), and shrimp sauce (shrimp bisque).
Also known as brown sauce, Espagnole begins with a mirepoix (carrots, celery, and onions), beef stock, and deglazed brown bits (fond) from beef bones. From there, tomato paste and spices may be added.
To make a demi-glace, a rich French brown sauce, combine the Espagnole with more beef stock; to create Bordelaise, a red wine sauce that pairs well with steak and mushrooms, mix the demi-glace with red wine and herbs. Serve this with fine steak for an excellent dinner.
Probably the first mother sauce you ever tasted (over a heaping bowl of spaghetti), tomato sauce is often a mixture of just onions, garlic, and tomatoes. Although some traditionalists may start with a roux, most tomato sauces merely rely on a tomato reduction to build flavor and create thickness.
Think of Hollandaise as a fancy warm mayonnaise that uses clarified butter in place of oil and gets drizzled over asparagus and eggs providing a buttery but tart flavor.. Instead of using a roux or a reduction, Hollandaise uses the method of emulsification: the act of using a binding agent (in this case, an egg yolk) to force two ingredients that don't mix well together, clarified butter and lemon juice. Hollandaise takes patience, as you must temper the mixture so that the eggs do not curdle. The sauce can break easily, but you can save it by adding a little heavy cream and whisking until the sauce returns to its smooth state. This takes practice!