Contributions to diophantine approximation in fields of series

The following topics are taken up: (i) the dimension of certain vector spaces defined in terms of denominations of differential polynomials, (ii) examples of series for which a Thue-Siegel-Roth type theorem holds, (iii) approximation of linear forms whose coefficients satisfy algebraic differential equations, and (iv) rational approximations to solutions of algebraic difference-differential equations.Written with partial support from NSF grant NSF-MCS 78-01770.