Compounds bearing two hydroxyl groups are known as diols. When the hydroxyl groups are located on adjacent carbon atoms, the diols are called vicinal diols or glycols. Under acidic conditions, vicinal diols undergo a specific reaction called pinacol rearrangement.
The reaction begins with transferring a proton from the acid catalyst to one of the hydroxyl groups, producing an oxonium ion.

Overview
Epoxides result from alkene oxidation, which can be achieved by a) air, b) peroxy acids, c) hypochlorous acids, and d) halohydrin cyclization.
Epoxidation with Peroxy Acids
Epoxidation of alkenes via oxidation with peroxy acids involves the conversion of a carbon–carbon double bond to an epoxide using the oxidizing agent meta-chloroperoxybenzoic acid, commonly known as MCPBA. Since the O–O bond of peroxy acids is very weak, the addition of electrophilic oxygen of peroxy acids to...

The Knoevenagel condensation is an aldol-type reaction involving the condensation of aldehydes or ketones with active methylene compounds such as β-diesters to produce substituted olefins.

Regular Claisen condensation involves the synthesis of β-ketoesters by combining identical ester molecules bearing two α hydrogens in the presence of an alkoxide base. The reaction commences with the deprotonation of the acidic α hydrogen by the base to form a resonance stabilized ester enolate. This nucleophilic ion then attacks the carbonyl center of another ester molecule to generate a tetrahedral alkoxide intermediate. Next, the expulsion of the alkoxide group from the intermediate restores...

Acetoacetic ester synthesis is a method to obtain ketones from alkyl halides and β-keto esters. The reaction occurs in the presence of an alkoxide base that abstracts the acidic proton of the β-keto esters. The step results in an enolate ion which is doubly stabilized. The enolate then reacts with an alkyl halide via the SN2 process to produce an alkylated ester intermediate with a new C–C bond. The hydrolysis of the intermediate, followed by acidification, results in an alkylated β-keto acid.

Malonic ester synthesis is a method to obtain α substituted carboxylic acids from ꞵ-diesters such as diethyl malonate and alkyl halides.