Béchamel, velouté, espagnole, hollandaise, and tomato are the five foundational sauces of classical French cuisine, known as the mother sauces because they serve as the base for countless smaller, derivative sauces.
Béchamel is a white sauce made by whisking hot milk into a butter-and-flour roux; it underlies dishes like lasagna and croque-monsieur. Velouté is a pale sauce made the same way but with a light stock (chicken, veal, or fish) instead of milk, and forms the base for sauces like supreme. Espagnole is a brown sauce built from a rich veal or beef stock, browned mirepoix, and tomato, and is the starting point for demi-glace and sauces such as bordelaise. Hollandaise is an emulsion of egg yolks and melted butter finished with lemon juice, used on dishes like eggs Benedict and asparagus. Tomato sauce, the fifth, is built from tomatoes, aromatics, and herbs and underlies much of Italian and Mediterranean cooking.
The five-sauce classification is credited to Auguste Escoffier, who in the early 20th century revised the shorter list of foundational sauces that Marie-Antoine Carême had codified a century earlier. The mother sauces remain the standard teaching framework in professional kitchens, even outside French cuisine.