This volume has been written for Professor Kunihiko Kodaira by his friends and students to mark the occasion of his sixtieth birthday.

As is well known, Kodaira has made decisive contributions to algebraic geometry and complex analysis, i. e., to the theory of algebraic varieties and of complex manifolds. Recently the Collected Works of Kodaira (three volumes) have been published by Iwanami Shoten, Publishers (Tokyo) and Princeton University Press (Princeton). In these three volumes, one may see how this remarkable mathematician has developed his ideas, establishing many results of fundamental importance in various branches of mathematics. Among the most distinguished works of Kodaira in algebraic geometry and complex manifolds are those in the theory of harmonic integrals and its application to algebraic and Kähler varieties, Kodaira's vanishing theorem and the projective imbedding of Hodge varieties, deformation theory (with D. Spencer), and the theory of compact, complex analytic surfaces.

It might perhaps be more appropriate to the occasion to offer a discussion of the mathematical works of Professor Kodaira ; however, there is a survey by one of the present editors in the preface of the said Collected Works. Therefore, we have included instead an introduction which gives a brief account of the development of complex analysis and algebraic geometry in these thirty years. Hopefully it will serve as background material for the subjects treated in the present volume, especially to those readers not previously familiar with this area.