Short answers, pulled from the story.
A fatty acid is a carboxylic acid with an aliphatic chain that is either saturated or unsaturated. Most naturally occurring fatty acids have an unbranched chain with an even number of carbon atoms, ranging from 4 to 28.
Michel Eugene Chevreul introduced the concept of fatty acid, acide gras, in 1813. He initially used variant terms including graisse acide and acide huileux, meaning acid fat and oily acid.
In a cis configuration the two hydrogen atoms next to a double bond sit on the same side of the chain, causing it to bend, while in a trans configuration they sit on opposite sides, leaving the chain nearly straight. Cis unsaturated fatty acids increase cell membrane fluidity, whereas trans unsaturated fatty acids do not.
Fatty acids are classified by the length of their aliphatic tails. Short-chain have five or fewer carbons, medium-chain have 6 to 12, long-chain have 13 to 21, and very long chain fatty acids have 22 or more carbons.
Cells of the central nervous system cannot take up free fatty acids from the blood because the blood-brain barrier is impervious to most of them, excluding only short-chain and medium-chain fatty acids. These cells must instead manufacture their own fatty acids from carbohydrates to maintain their membranes.
The two essential fatty acids are linoleic acid and alpha-linolenic acid, which the human body cannot make in sufficient quantity and must obtain from food. They are widely distributed in plant oils.
Fatty acids are mainly used in the production of soap, both for cosmetic purposes and, as metallic soaps, as lubricants. They are also converted via their methyl esters into fatty alcohols and fatty amines, which serve as precursors to surfactants, detergents, and lubricants.