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Fatty acids are long-chain carboxylic acids typically 12-20 carbons long, consisting of a hydrophobic hydrocarbon tail and a hydrophilic carboxyl head group. Saturated fatty acids (no C=C bonds) are linear and pack densely; unsaturated fatty acids contain one or more C=C double bonds (cis or trans), introducing kinks that affect packing and fluidity. The positions and stereochemistry of double bonds are critical: cis double bonds are found in biological fatty acids, while trans fatty acids (from industrial processes or ruminant metabolism) are associated with adverse health effects.
From your study of organic chemistry, you know that carboxylic acids have a –COOH head group and that carbon chains can vary in length and saturation. A fatty acid is simply a carboxylic acid with a long hydrocarbon tail — typically 12 to 20 carbons. That tail is overwhelmingly hydrophobic, which is why fatty acids don't dissolve well in water despite having a polar head. This amphipathic character — one end water-loving, the other water-fearing — is the structural basis for membranes, micelles, and fat storage.
The first major classification axis is saturation. A saturated fatty acid like palmitic acid (16:0) has no carbon-carbon double bonds: every carbon in the chain holds as many hydrogens as possible. The result is a straight, flexible chain that can pack tightly against neighboring chains, much like uncooked spaghetti stacking neatly in a box. This tight packing is why saturated fats — butter, lard, coconut oil — are solid at room temperature. An unsaturated fatty acid contains one or more C=C double bonds. Each *cis* double bond introduces a rigid ~30° kink in the chain, preventing tight packing. Oleic acid (18:1Δ9) has one kink; linolenic acid (18:3Δ9,12,15) has three. More kinks mean looser packing and lower melting points, which is why vegetable oils are liquid at room temperature.
The cis versus trans distinction matters enormously. Nearly all naturally occurring unsaturated fatty acids have *cis* geometry — the two hydrogens on the double-bond carbons point the same direction, forcing the kink. Trans fatty acids, produced mainly by industrial partial hydrogenation, have hydrogens on opposite sides of the double bond. This straightens the chain back out, mimicking saturated fat packing, which is why trans fats raise LDL cholesterol and cardiovascular risk despite being technically "unsaturated."
Fatty acids are also classified by where the first double bond falls, counting from the methyl (omega) end of the chain. Omega-3 fatty acids (first double bond at carbon 3 from the methyl end) include α-linolenic acid, EPA, and DHA; omega-6 fatty acids (first double bond at carbon 6) include linoleic and arachidonic acid. Humans cannot introduce double bonds beyond carbon 9 from the carboxyl end, making omega-3 and omega-6 fatty acids essential — they must come from the diet. This classification system connects fatty acid structure directly to nutritional biochemistry and to the synthesis of signaling molecules like prostaglandins and leukotrienes that you will encounter in lipid metabolism.