He obtained his PhD from the University of Tokyo in 1949, with a thesis entitled Harmonic fields in Riemannian manifolds.

In 1949 he travelled to the Institute for Advanced Study in Princeton, New Jersey at the invitation of Hermann Weyl.

Kodaira rapidly became involved in exploiting the tools it opened up in algebraic geometry, adding sheaf theory as it became available.

In a second research phase, Kodaira wrote a long series of papers in collaboration with Donald C. Spencer, founding the deformation theory of complex structures on manifolds.

This gave the possibility of constructions of moduli spaces, since in general such structures depend continuously on parameters.

This resulted in a typology of seven kinds of two-dimensional compact complex manifolds, recovering the five algebraic types known classically; the other two being non-algebraic.