Mono- and di-derivatives of cyclodextrins are completely defined, also a method for their synthesis and purification, functionalised cyclodextrins obtained from these derivatives, and the synthesis of supports comprising these cyclodextrin derivatives. Use of the supports for the preparation of separation of enantiomers, for asymmetric synthesis, for catalysis, for the preparation or separation of geometrical isomers or positional isomers, or for the preparation or separation of organic molecules with a hydrophobic nature is also described.