Fatty acids are carboxylic acids with a -COOH group and quite a long hydrocarbon chain attached.

Stearic acid - C₁₇H₃₅COOH - is an example of a saturated fatty acid - all carbon atoms in the main chain being linked by single carbon-carbon bonds. Its IUPAC name is octadecanoic acid and its lipid number code is C18:0. It is a waxy solid with a melting point of 69 °C.

Oleic acid - C₁₇H₃₃COOH - has the same number of carbon atoms, but one double bond halfway along the main chain, which makes it unsaturated (monounsaturated). Its IUPAC name is (Z)-Octadec-9-enoic acid, and its lipid number code is 18:1 cis-9. It is an oily liquid with a melting point of 13 °C.

This double carbon-carbon bond means oleic acid has 2 less hydrogen atoms than stearic acid, and this gives it a noticeable kink. However the two single hydrogen atoms on either end of the bond are in the cis configuration, as both they are on the same side. This is more favourable than its isomer elaidic acid [see below] which is a trans fatty acid.

Polyunsaturated fatty acids have more than one double bond. Examples on this site :

This molecule - elaidic acid - is an unsaturated fatty acid. It has a double bond half way along the hydrocarbon tail. It is an isomer of oleic acid (see above). Its IUPAC name is (E)-octadec-9-enoic acid.
However the single hydrogen atoms on either side of this bond are facing directly away from one another - a position known as trans. The shape of the molecule is fairly 'straight' - more like stearic acid than oleic acid. All the atoms immediately adjacent to the double bond are in the same plane and their bonds are spaced out fairly evenly so the carbon atoms nearest to the two forming the double bond are in a straight line when seen from the edge .... back to face-on . This causes the fatty acid tails to pack together quite closely, and gives a product with a high density. It is an oily solid, and its melting point is 45 °C.

The glyceryl ester of elaidic acid - the major 'trans fat' - is formed as a by-product of the hydrogenation of oils in the production of margarine and spreads, as well as processed foods such as biscuits and cakes. This industrial process using metallic catalysts at high pressure was aimed at converting cheap oils of plant origin into products with higher melting and boiling points, also less likely to become rancid, to act as substitute for animal products. It has been found that the level of trans fat in the product of this process may be altered by modification of pressure used, the temperature and the length of time during hydrogenation.
Elaidic acid is also present to a much lesser extent as a natural component of some animal fats. It has been linked to increases in cholesterol in consumers as it lowers high-density lipoprotein (HDL) - commonly known as "good cholesterol", and it may consequently cause health conditions such as coronary heart disease, heart attacks and strokes.

The United States Food and Drug Administration (FDA) declared that partially hydrogenated oils (which contain trans fats) are not "generally recognized as safe", and set in train plans to remove them from all American processed foods from June 2018. However blended products containing less than 0.5 grams of trans fats per serving can evade this restriction.