The proceedings of the Katata Symposium 1982,reflect the present state of research onclassification problems. In addition to papers onthe classification theory of algebraic and analyticmanifolds, the volume contains papers onalgebraic and analytic surfaces, and periodmappings. It also contains a chapter listing openproblems in the field, indicating the ample timedevoted to them during the symposium.Preface.List of Participants.ContentsSome remarks on Kahler manifoldswi th c l = 0...............................On the period map of surfaces withK 2 = X = 2................................Deformations of surfaces containingglobal spherical shells...................Canonical rings of algebraic varieties....On primitively symplectic compact KahlerV-manifolds of dimension four.............Asymptotic fibrations of complexvarieties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 251Algebraic surfaces with positiveindices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 281Some remarks on the moduli ofK3 surfaces............................... 303VII O surfaces and a duality ofcusp singularities........................ 333Surjectivity of period map forK3 surfaces............................... 379Infinitesimal variations of Hodge structureand the generic Torelli problem for projectivehyper surfaces ( after Carlson, Donagi, Green,Griffiths, Harris)........................ 399Configurations of -2 rational curves onhyperplane sections of projectivethreefolds............. ......... ..... ..... 465The structure of open algebraicsurfaces. II............................... 499Degenerations of elliptic surfaces andcertain non Kahler manifolds..............Weak positivity and the additivity ofthe Kodaira dimension, II : The localTore 11 i map.....................:.........Open Problems.