This collection of papers on function theory and function-theoretic methods in partial differential equations is split into three main groups of topics. The first group contains results on elliptic and some related partial differential equations which are obtained by complex analytic methods, eg. Bergman and Vekua integral operator methods, differential transformation methods, associated operators for initial value problems of Cauchy Kowalewski type, and reproducing kernels. Quaternionic analytic methods and concepts in Clifford analysis are also presented. The second group includes papers on classical complex analysis, including geometric function theory, singularities of series in special polynomials, and subharmonic functions. The last group of papers deal with the Riemann and the riemann-Hilbert boundary value problems, respectively for analytic functions, for first order elliptic equations, for pseudoparabolic equations, for an overdetermined elliptic system, and for the three dimensional counterpart of the Cauchy-Riemann system, the Moisil-Theodorescu system, and in Clifford analysis.It is aimed at students and specialists working in real and complex analysis and partial differential equations.