The reverse of the aldol addition reaction is called the retro-aldol reaction. Here, the carbon–carbon bond in the aldol product is cleaved under acidic or basic conditions to form two molecules of carbonyl compounds. The mechanism of the reaction consists of three steps.
In the first step, as depicted in Figure 1, the base deprotonates the β-hydroxy ketone at the hydroxyl group to form an alkoxide ion.

The Claisen rearrangement is a [3,3] sigmatropic rearrangement of allyl vinyl ethers to unsaturated carbonyl compounds. The rearrangement is a concerted pericyclic reaction proceeding via a chair-like transition state.

Robinson annulation is a base-catalyzed reaction for the synthesis of 2-cyclohexenone derivatives from 1,3-dicarbonyl donors (such as cyclic diketones, β-ketoesters, or β-diketones) and α,β-unsaturated carbonyl acceptors. Named after Sir Robert Robinson, who discovered it, this reaction yields a six-membered ring with three new C–C bonds (two σ bonds and one π bond).

Just like β-keto acids—which upon thermal decarboxylation form ketones—β-dicarboxylic acids undergo decarboxylation to generate monocarboxylic acids with the liberation of carbon dioxide.

By replacing an α-hydrogen with a halogen, acid-catalyzed α-halogenation of aldehydes or ketones yields a monohalogenated product
In the first step of the mechanism, the acid protonates the carbonyl oxygen resulting in a resonance-stabilized cation, which subsequently loses an α-hydrogen to form an enol tautomer. The C=C bond in an enol is highly nucleophilic because of the electron-donating nature of the –OH group. Consequently, the double bond attacks an electrophilic halogen to form a...

The Cope rearrangement is classified as a [3,3] sigmatropic shift in 1,5-dienes, leading to a more stable, isomeric 1,5-diene. The reaction involves a concerted movement of six electrons, four from two π bonds and two from a σ bond, via an energetically favorable chair-like transition state.