Selected works of Ellis Kolchin with commentary

Picard-Vessiot theory of partial differential fields The notion of dimension in the theory of algebraic differential equations Part I. The Papers of Ellis Kolchin: On certain ideals of differential polynomials On the basis theorem for infinite systems of differential polynomials On the exponents of differential ideals On the basis theorem for differential systems Extensions of differential fields. I Extensions of differential fields. II Algebraic matric groups The Picard-Vessiot theory of homogeneous linear ordinary differential equations Extensions of differential fields. III Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations On certain concepts in the theory of algebraic matric groups Existence theorems connected with the Picard-Vessiot theory of homogeneous linear ordinary differential equations Algebraic groups and differential equations Two proofs of a theorem on algebraic groups Picard-Vessiot theory of partial differential fields Galois theory of differential fields Differential fields and group varieties (First lecture) Differential fields and group varieties (Second lecture) On the Galois theory of differential fields Algebraic groups and the Galois theory of differential fields Rational approximation to the solutions of algebraic differential equations Existence of invariant bases Abelian extensions of differential fields Le theoreme de la base finie pour les polynomes differentiels The notion of dimension in the theory of algebraic differential equations Singular solutions of algebraic differential equations and a lemma of Arnold Shapiro Some problems in differential algebra Algebraic groups and algebraic dependence Differential polynomials and strongly normal extensions Constrained extensions of differential fields Differential equations in a projective space and linear dependence over a projective variety Differential algebraic groups Differential algebraic structures On universal extensions of differential fields Differential algebraic groups A problem on differential polynomials Painleve transcendent Part II. Commentary: Algebraic groups and Galois theory in the work of Ellis R. Kolchin by A. Borel Direct and inverse problems in differential Galois theory by M. F. Singer Les corps differentiellement clos, compagnons de route de la theorie des modeles by B. Poizat Differential algebraic geometry and differential algebraic groups: From algebraic differential equation to Diophantine geometry by A. Buium and P. J. Cassidy.