Thickening
Thickening is mostly starch granules swelling in heat — or gelatin and reduction doing the work instead. These are the agents, the ratios, and the doneness test.
Roux
Equal parts fat and flour by weight, cooked together before use. The longer you cook it the more flavour and colour it has — and the less it thickens, so dark roux needs more of it.
Slurry
Cornstarch stirred into cold liquid (about 1 tablespoon per cup), then whisked into the simmering pot. Add it cold or it seizes into lumps.
Beurre manié
An uncooked roux — equal soft butter and flour kneaded to a paste — whisked into a hot liquid at the end to thicken and gloss a sauce in minutes.
Nappe
Not an agent but the doneness test: the sauce coats the back of a spoon, and a finger drawn through holds a clean line before it fills back in.
Liaison
An enrichment of egg yolk and cream stirred in off strong heat. It thickens gently and adds silk — but it curdles if it boils.
Gelatin
Collagen melted out of bones and connective tissue. It is why a real stock sets to a wobble and bodies a sauce with no starch at all. More: Stock →
Cornstarch vs flour
A cornstarch slurry sets clearer and glossier and thickens with less; flour is cloudier but more stable and less prone to thinning if it overcooks.
More: Stock →Thicken without an agent: Reducing →Deglazing →
