A roux is a cooked mixture of flour and fat that forms the base of sauces such as béchamel, velouté and espagnole. (See Sauces)
Generally made with equal parts of melted butter and flour, the two are cooked together over a medium flame until the flour is cooked out.
Liquids (milk, broth or stock) are the added to the cooked butter/ flour blend to create the base of the sauce. The less liquid added the thicker the sauce.
In classic French cuisine, of the five mother sauces i.e. those from which other sauces are made from, the three listed in the article header all have a roux as their base, so chef’s should have this technique mastered as part of their repertoire.
Naturally, with its French roots, cajun cuisine from US states such as Louisiana also incorporates roux into famous dishes such as gumbo and étouffée, although the roux is generally made with bacon grease or oil rather than butter, and the roux is cooked to a much darker brown colour enhancing these dishes rich flavour.
With the prevalence of pork across central Europe, lard is used as the fat portion of the roux in countries e.g. Poland, Germany and Hungary.