What are the (most common) different ways to thicken sauces and gravies?

Question

I know of a few ways to thicken sauces and the like:

• Egg (protein)
• Flour (protein / starch)
• Starch (cornstarch etc)
• Reduction (reducing watery component)

Are these the only common ones, or what else should a cook keep in his repetoire?

Answer

Major ways of thickening a sauce -- or, for that matter, some other liquid:

• Starch (e.g., flour, cornstarch, tapioca, arrowroot)
• Emulsion (e.g., butter, cream, yolk, mustard, blending in lecithin-and-fat)
• Coagulated protein (e.g., blood, egg, pureed seafood)
• Gels/polysaccharides (gelatin, alginate, xanthan, pectin, agar agar, guar gum)
• Suspension (general puree of solids)

Note that some of the examples of one category can also fit into another.

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