In 1868 he finished Tbilisi First Gymnasium and in 1872 Novorossiya University, faculty of Physics and mathematics, department of Natural Sciences. In 1873 he is abroad were he acquainted L.Mayer's and Vilicenuce's laboratories. In 1876 he started working in the chemical laboratory of Novorossiya University. In 1881 he became Magister of the chemistry and in 1885 he became Doctor of the Chemistry. In 1884 he was a docent and from 1885 until 1917 he was Professor of Novorrossiya University.
His works in Organic Chemistry developed Stereochemical Theory. Melikishvili discovered one of the class of organic compounds Glycidacids (named by him). The second cycle of his works are about Inorganic Chemistry. Melikishvili with his pupil L. Pizarjevski synthesized superacids of some elements (U, Nb, Ta, W, Mo, B, Ti, V) (1897–1913). they also showed that from many supposed formulas of Hydrogen Peroxide the correct is H-O-O-H.
In Tbilisi State University