French Cuisine Mother Sauces and more

French cuisine has 5 Mother Sauces, the basis for all other sauces. The 5 Mother Sauces are:
Béchamel Sauce - If you have milk, flour, and butter you can make a very basic béchamel.
Velouté Sauce - Another simple sauce made by thickening white stock (usually chicken stock) with a roux and then simmering it for a while.
Espagnole Sauce - Also called Brown Sauce, a slightly more complex mother sauce. Expagnole is made by thickening brown stock with a roux. So in that sense, it's similar to a velouté. The difference is that Espagnole is made with tomato purée and mirepoix for deeper color and flavor.
Hollandaise Sauce - Hollandaise is unlike the mother sauces we've mentioned so far, due to a liquid and a thickening agent, plus flavorings. Hollandaise is a tangy, buttery sauce made by slowly whisking clarified butter into warm egg yolks.
Classic Tomate Sauce - This sauce resembles the traditional tomato sauce that we might use on pasta and pizza, but it's got much more flavor and requires a few more steps to make.

Mire Poix – A flavor base made from diced vegetables cooked—usually with butter, oil, or other fat—for a long time on low heat without coloring or browning. It is not sautéed or otherwise hard cooked, because the intention is to sweeten the ingredients rather than caramelize them. Usually the vegetable mixture is 50% onion, 25% carrot and 25% celery
Bouquet Garni - A bundle of herbs usually tied together with string and mainly used to prepare soup, stock, casseroles and various stews. The bouquet is cooked with the other ingredients, but is removed prior to consumption. Most French recipes include thyme, bay leaf and parsley. Pepper corns are also often included. Combine the 8-10 pepper corns, 1 sprig fresh thyme, 3-4 sprigs fresh parsley, and 1 bay leaf in cheesecloth and tie with kitchen twine