Most classic sauces are variations on a handful of base sauces, and the idea is not only French: Germany, Japan, India, Mexico, Korea, and China each have their own bases (see below). Learn the base and its thickener, and the derivatives are just a few added ingredients. Antonin Carême named four "mother sauces" (Espagnole, Velouté, Allemande, Béchamel) in the early 1800s; Auguste Escoffier trimmed that to the five below around 1900, demoting Allemande to a velouté derivative and adding Sauce Tomate and Hollandaise.

Each of these starts from demi-glace and adds a reduction of wine or vinegar, aromatics, and a finishing touch. The method is nearly always the same: reduce the flavoring ingredients almost dry, add the demi-glace, simmer briefly, strain if needed, and finish with butter off the heat.

An emulsion holds fat and water together in a smooth suspension, normally by whisking a fat into a liquid with an emulsifier (egg yolk's lecithin, or the proteins in butter solids). These do not need a roux; they are stabilized by technique and temperature instead.

These are not "mother sauces" in the French sense of five fixed recipes, but each does the same job: one base, made ahead or kept on hand, that many dishes branch from. Several do it with a different thickener (nuts, ground chiles, fermented beans, caramelized sugar), which is a useful contrast with the roux and emulsions above.

Not bases that branch into families, but sauces that appear again and again: