  This work deals with special nested objects arising in massive higher order
perturbative calculations in renormalizable quantum field theories. On the one
hand we work with nested sums such as harmonic sums and their generalizations
(S-sums, cyclotomic harmonic sums, cyclotomic S-sums) and on the other hand we
treat iterated integrals of the Poincar\'e and Chen-type, such as harmonic
polylogarithms and their generalizations (multiple polylogarithms, cyclotomic
harmonic polylogarithms). The iterated integrals are connected to the nested
sums via (generalizations of) the Mellin-transformation and we show how this
transformation can be computed. We derive algebraic and structural relations
between the nested sums as well as relations between the values of the sums at
infinity and connected to it the values of the iterated integrals evaluated at
special constants. In addition we state algorithms to compute asymptotic
expansions of these nested objects and we state an algorithm which rewrites
certain types of nested sums into expressions in terms of cyclotomic S-sums.
Moreover we summarize the main functionality of the computer algebra package
HarmonicSums in which all these algorithms and transformations are implemented.
Furthermore, we present application of and enhancements of the multivariate
Almkvist-Zeilberger algorithm to certain types of Feynman integrals and the
corresponding computer algebra package MultiIntegrate.
