This work is the first in a two-volume complementary set taken from the proceedings of a conference held in Regensburg in 1995 on the subject of operatory theory and its applications. It covered different aspects of linear and nonlinear spectral problems, starting with problems for abstract operators up to spectral theory of ordinary and partial operators, pseudodifferential operators, and integral operators. The workshop was also focused on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems. The applications concerned applications to mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems. This volume contains the contributions dedicated to the theory of differential and integral operators.