Father Grigol Melikishvili was a public figure and actively participated in the establishment of the first private Georgian printing house in Tbilisi.

His younger brother Iosebi was also a publisher, and his sister, Sergei Meskhi's wife, Ekaterine Melikishvili-Meskhi, was a writer, translator and feminist.

Ilia Chavchavadze, Akaki Tsereteli, Sergey Meskhi, Niko Nikoladze and other leaders of the Georgian intelligentsia often visited the Melikishvili family.

Petre Melikishvili graduated from the gymnasium with honors in 1868 and under the influence of Besarion Ghoghoberidze chose to study natural sciences.

In 1869 he left for Ukraine and enrolled in the Department of Natural Sciences of the Faculty of Physics and Mathematics at the University of Odessa.

Vasil Petriashvili (later the rector of Odessa University) also studied in the last year of the Faculty of Physics and Mathematics, with whom Petre Melikishvili soon became friends.

In 1878 he passed the master's examinations at the University of Odessa and began intensive work on products of unsaturated acids.

[5] In 1881, Petre Melikishvili defended his dissertation "Acrylic Acids" for a master's degree, after which he left for Paris, where he attended lectures by the French chemist Marceline Bertha.

Petre Melikishvili left France for Munich, where he worked in the laboratory of the German chemist Adolf Bayer.

In 1885, Melikishvili defended his dissertation "Isomeric Crotonic Acid Products" and was awarded the degree of Doctor of Chemistry.

During this period Petre Melikishvili worked on the synthesis of homologous series of acrylic acid and their products.

Petre Melikishvili laid the foundation for the creation of chemical terminology in the Georgian language, which was later developed by his students: Nino Tsitsishvili and Rusudan Nikoladze.

The Migay meteorite differed from others in that it contained coal, sulfur, phosphorus, and organic compounds, namely higher hydrocarbons.

As a result of chemical analysis of wine and wheat, he concluded that the quality of these products is influenced by climatic conditions and time.

"[5] At the suggestion of Ivane Javakhishvili, on January 13, 1918, Petre Melikishvili was elected the first rector of Tbilisi State University.

Petre Melikishvili applied for the resignation,[9] however, he continued to work in the Department of Organic Chemistry and headed the newly established Faculty of Agriculture of the University.