This volume contains a collection of 30 of the 51 papers that David Mumford wrote in algebraic geometry. The volume divides Mumford¿s papers into three broad areas, each preceded by an easy summarizing the results and outlining their influence on further developments by David Gieseker, George Kempf, Herbert Lange and Eckart Viehweg.

Further generations of researchers in this field, graduate students, mathematical physicists, and mathematical historians will profit a great deal from this collection of selected papers.

David Mumford was Professor of Applied Mathematics at Brown University.  In 1974 he was awarded the Fields Medal at the International Congress of Mathematicians in Vancouver.  In 2010 he was awarded the National Medal of Science.

Part I. Geometric Invariant Theory and the Moduli of Curves.- 1 An elementary theorem in geometric invariant theory (1961).- 2 Projective invariants of projective structures and applications (1962).- 3 Periods of a moduli space of bundles on curves (1968).- 4 The structure of the moduli spaces of curves and abelian varieties (1970).- 5 An analytic construction of degenerating curves over complete local rings (1972).- 6 Pathologies IV (1975).- 7 Stability of projective varieties (1977).- 8 On the Kodaira dimension of the moduli space of curves (1982).- 9 Towards an enumerative geometry of the moduli space of curves (1983).- Part II. Theta Functions and the Moduli of Abelian Varieties.- 10 On the equations defining abelian varieties. I (1966).- 11 On the equations defining abelian varieties. Il (1967).- 12 On the equations defining abelian varieties. III (1967).- 13 Families of abelian varieties (1966).- 14 A note on Shimura's paper "Discontinuous groups and abelian varieties" (1969).- 15 Theta characteristics of an algebraic curve (1971).- 16 An analytic construction of degenerating abelian varieties over complete rings (1972).- 17 A rank 2 vector bundle of P4 with 15,000 symmetries (1973).- 18 Prym Varieties I (1974).- 19 A new approach to compactifying locally symmetric varieties (1973).- 20 Hirzebruch's Proportionality Theorem in the non-compact case (1977).- 21 On the Kodaira dimension of the Siegel modular variety (1983).- Part III. The Classification of Surfaces and Other Varieties. -  22 Enriques' classification of surfaces in char p: I (1969).- 23 Enriques' classification of surfaces in char p: II (with E. Bombieri) (1979).- 24 Enriques' classification of surfaces in char p: III (with E. Bombieri) (1976).- 25 Pathologies of modular algebraic surfaces (1961).- 26 Further pathologies in algebraic geometry (1962).- 27 Pathologies III (1967).- 28 Rational equivalence of 0-cycles on surfaces (1969).- 29 Some elementary examples of unirational varieties which are not rational (1972).- 30 An algebraic surface with K ample, (K2) = 9, pg = q = 0 (1979).