The French mother sauces are a group of five basic sauces that serve as the foundation for many other sauces. They were first codified by Auguste Escoffier, a French chef, in the early 20th century. The five mother sauces are:

1. Béchamel sauce: a white sauce made from a roux (butter and flour) and milk. It is often flavored with onion, bay leaf, and nutmeg.

2. Velouté sauce: a light-colored sauce made from a roux and chicken, veal, or fish stock. It can be flavored with herbs, lemon juice, or wine.

3. Espagnole sauce: a brown sauce made from browned beef bones, vegetables, and tomato paste. It is then simmered in a beef or veal stock, and strained.

4. Hollandaise sauce: an emulsion of egg yolks, butter, lemon juice, and white wine vinegar. It is typically served with eggs Benedict, asparagus, or fish.

5. Sauce tomate: a tomato-based sauce made from sautéed onions and garlic, canned tomatoes, and a bouquet garni. It can be used as a base for other sauces, or as a sauce on its own.

These five mother sauces can be used to make a vast array of other sauces by adding various ingredients such as herbs, spices, wine, cream, or stock.