Tbilisi State University, student, 1931-1932;

Moskow State University, Student, 1932-1937;

Post graduate (Aspirant) 1937-1939.

Candidate of Sciences (PhD), 1939, Moskow State University;

Doctor of Sciences (Habilitation), 1945, Steklov Mathematical Institute, Moskow.

Corresponding member of the Georgian Academy of Sciences, 1956,

Academician of the Georgian Academy of Sciences, 1960.

1940 - 1998 Mathematical Institute of Georgian Academy of Sciences;

1962 - 1989 Head of Department of Geometry and topology;

1946 - 1998 Chair of Algebra and Geometry at Tbilisi State University.

1. On a theorem in the theory of dimensionality. (English) Compositio Math. 5, 292-298 (1937).

2. On level surfaces and domains of smaller values of a function defined on a bounded manifold. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 24, 635-639 (1939).

3. On the variation of Betti numbers of a moving level surface. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 22, 293-297 (1939).

4. On the homology theory of topological space. (English) Mitteil. Georg. Abt. Akad. Wiss. USSR 1, 337-340 (1940).

5. On Schnirelmann's transformations. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 30, 199-203 (1941).

6. Ueber Konvergenzraeume. (Russian. German summary) Rec. Math. Moscou, n. Ser. 9, 377-383 (1941).

7. Behavior of some topological invariants on level surfaces. Bull. Acad. Sci. Georgian SSR, 3 , 995-999 (1942).

8. The Betty groups of domains of smaller values. Bull. Acad. Sci. Georgian SSR, 4 , 853-859 (1943).

9. On the duality law in normal spaces. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 48, 233-235 (1945).

10. Theoreme de dualite pour le polyedre infini. (French) C. R. Acad. Sci., Paris 221, 15-17 (1945).

11. On duality relations in topological spaces. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 46, 131-132 (1945).

12. The duality law for retracts. (English) C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 51, 91-94 (1946).

13. On duality relations in topological spaces. Uspehi Mat. Nauk, 46, 131-132 (1946).

14. On level surfaces and regions of smaller values. Bull. Acad. Sci. Georgian SSR, 17 , 203-243 (1949).

15. Ueber Homologieapproximationen und Dualitaetssaetze fuer beliebige Mengen. (Russian) Mat. Sb., n. Ser. 28(70), 89-118 (1951).

16. On the equivalence of functional and spectral theory of homology. Izv. Akad. Nauk SSSR, Ser. Mat., 15, 421-438 (1951).

17. On the fundamental homomorphisms of duality. Akad. Nauk. Gruzin. SSR, Trudy Mat. Inst. Razmadze, 18, 1-52 (1951).

18. On spectrally singular homology groups. Soobsh. Acad. Nauk Gruzin. SSR, 14, 583-588 (1953).

19. Zur Anwendung der direkten Spektren bikompakter Gruppen in der Theorie der Homologien. (Russian) Soobshch. Akad. Nauk Gruz. SSR 15, 655-662 (1954).

20. On the application of direct spectra of bicompact groups in homology Theory. Soobsh. Acad. Nauk Gruzin. SSR, 15 , 655-662 (1954).

21. On Cech groups of infinite chains and finite cochains. Soobsh. Acad. Nauk Gruzin. SSR, 19, 5 , 513-520 (1957).

22. Generalization of the Steenrod duality rule. Soobsh. Acad. Nauk Gruzin. SSR, 21 , 641-648 (1958).

23. Homology groups of an infinite complex. Soobsh. Acad. Nauk Gruzin. SSR, 23 , 641-648 (1959).

24. Singular homology groups with compact coefficient group. Soobsh. Acad. Nauk Gruzin. SSR, 25, 641-648 (1960).

25. On homology theory of non-closed sets (English)[CA] General Topology and its Relations to modern Analysis and Algebra, Proc. Sympos. Prague 1961, 123-132 (1962).

26. Generalized products and limits and their applications in homology theory (English. Russian original) Russ. Math. Surv. 21, No.4, 13-23 (1966); translation from Usp. Mat. Nauk 21, No.4(130), 23-34 (1966).

27. Homology theory of noncompact spaces (Russian) [CA] Tr. IV Vsesoyuz. Mat. S"ezda, Leningrad 1961, 2, 57-62 (1964).

28. Sur les groupes d'homologie de l'espace, bases sur une categorie donnee de complexes (French) [CA] Topol. Appl., Symp. Herceg-Novi (Yugoslavia) 1968, 109 (1969).

29. On projective homology and homotopy groups. (English) [CA] Topics in Topol., Colloqu. Keszthely 1972, Colloquia Math. Soc. Janos Bolyai 8, 155-164 (1974).

30. On the construction of a functor generated by homology. (Russian) Soobshch. Akad. Nauk Gruz. SSR 92, 273-276 (1978).

31. On the properties of a functor generated by homology. (Russian) Soobshch. Akad. Nauk Gruz. SSR 94, 529-532 (1979).

32. On properties of D-functors generated by cohomologies. (Russian) Soobshch. Akad. Nauk Gruz. SSR 99, 529-532 (1980).

33. On D-functors. (Russian) Soobshch. Akad. Nauk Gruz. SSR 104, 529-532 (1981).

34. On the relation of D-functors to analogous functors. (Russian) Soobshch. Akad. Nauk Gruz. SSR 108, 473-476 (1982).