Why is roux a sauce used for thickening?

Actually, a roux is not a sauce, but is the base for several different sauces and is used as a thickener in many dishes. A roux is made by combining equal parts of fat and starch (usually butter or lard and flour) and cooking it in a pan until the flour taste has been cooked out. The color of a roux depends upon the amount of time you cook it - and the darker the roux, the more flavor it imparts to the dish you are using it in. By adding milk to a roux you are making a bechamel sauce which is used in many lasagna recipes and other dishes. Bechamel sauce is also the base sauce for several other culinary sauces: Mornay sauce (cheese sauce), Mustard sauce, and Sauce Soubise (contains finely chopped onions that are sweated in butter before adding to the sauce) are a few of these.