In the area of geometric and combinatorial configurations we showed that weakly flag-transitive configurations are in one-to-one correspondence with bipartite 1/2-arc-transitive graphs of girth 6 or more. We constructed several infinite families of weakly flag-transitive configurations, including some which are not self-polar. The smallest weakly flag-transitive configuration that we constructed has 27 points, and the smallest such non-self-polar configuration has 34 points. Using several computers in Ljubljana, Bielefeld and Bayreuth in parallel, we enumerated all v 3 configurations for v lower than is 19, and all triangle-free v 3 configurations for v lower than is 21. We worked out a theory of polycyclic configurations which generalize cyclic configurations and can be described by means of covering graphs having a cyclic group. This gave us a tool for the study of realizations of combinatorial configurations in the euclidean plane. We investigated links between the polycyclic structure of configurations on one hand, and cages (especially 10-cages) on the other hand. The polycyclic v k configurations for k is 2,3,4 were explored in more detail. In some cases their algebraic structure can be used to describe their rotational realization in the euclidean plane. It turned out that for certain polycyclic v 4 configurations their combinatorial description uniquely determines the existence of their rotational realization. In the area of theoretical chemistry we designed a generalized spiral code which can be used to represent any cubic polyhedron efficiently. We worked out the basic theory of cyclic Haar graphs and applied it to investigate the symmetry properties of certain molecular graphs on the torus. By means of generating functions we computed Hosoya polynomials for various families of graphs corresponding to benzenoid molecules. We developed algorithms for reconstruction of molecular graphs which utilize not only the lengths of the bonds but also the angles among them, thus achieving greater reliability and robustness. In the area of symbolic computation we generalized Gosper's summation algorithm to the case when the summand is both hypergeometric and multibasic q-hypergeometric. We developed algorithms for finding polynomial and hypergeometric solutions of recurrences in the multibasic and mixed case. We worked out a theory of solving linear operator equations by expanding solutions into polynomial series where the polynomial basis is compatible with the operator. We showed that this yields an isomorphism of the corresponding operator algebras, which was then used to find solutions of operator equations in the form of series with polynomial, rational, and hypergeometric coefficients. We investigated solutions of multivariate linear recurrences with constant coefficients. To such a recurrence we assigned its apex, which together with the initial conditions determines the algebraic nature of the generating function of its solution. We constructed examples where the generating function is D-finite but not algebraic, and other examples where this function is not D-finite. We determined the structure of multivariate hypergeometric terms, and proved a slightly modified Wilf-Zeilberger conjecture that every holonomic hypergeometric term is conjugate to a proper term. We constructed examples of holonomic hypergeometric terms which are not proper, and designed an algorithm which computes the minimal additive decomposition of a univariate hypergeometric term. In the theory of relative realizability we studied computable analysis and topology. Partial combinatory algebras with subalgebras of computable elements were used as models of computation on which we based categories of modest sets. We showed that domains with totalities embed into equilogical spaces, and that this embedding preserves simple and dependent types. We demonstrated how computable analysis and topology can be developed in the inner logic of modest sets.