Moduli Theory and Classification Theory of Algebraic Varieties Moduli theory of algebraic varieties and classification theory of compact complex spaces Moduli spaces for polarized algebraic varieties Group quotients in the category of analytic spaces and the category of algebraic spaces Applications of the quotient theorems to moduli of algebraic varieties Quotients for affine schemes by reductive algebraic groups Quotients in the category of schemes Mumford’s construction of the moduli variety for curves and polarized abelian varieties. Other applications of Mumford’s quotient theory Other methods of treating moduli problems. Artin’s method of algebraic stacks. Griffiths’s method of period maps Compactification of moduli spaces Fine moduli spaces. The universal families for stable curves with level n structure Applications of moduli theory to fibre spaces and the additivity formula for the Kodaira dimension of fibre spaces. Open problems.