The structure of commuting elements in an algebra is of fundamental importance for its structure and representation theory as well as for its applications. The main objects studied in this monograph are q-deformed Heisenberg algebras - more specifically, commuting elements in q-deformed Heisenberg algebras. In this book the structure of commuting elements in q-deformed Heisenberg algebras is studied in a systematic way. Many results are presented with complete proofs. Several appendices with some general theory used in other parts of the book include material on the Diamond lemma for ring theory, a theory of degree functions in arbitrary associative algebras, and some basic facts about q-combinatorial functions over an arbitrary field. The bibliography contains, in addition to references on q-deformed Heisenberg algebras, some selected references on related subjects and on existing and potential applications. The book is self-contained, as far as proofs and the background material are concerned Right Focal Point Boundary Value Problems for Functional-Differential Equations / R. P. Agarwal and Q. Sheng -- The Ideas and Methods of the Perm Seminar on Boundary Value Problems / N. V. Azbelev -- On Extension of the Vallee-Poussin Theorem to Equations With Aftereffect / N. V. Azbelev and L. F. Rakhmatullina -- Initial-Boundary Value Problems for Impulsive Parabolic Functional Differential Equations / D. Bainov, Z. Kamont and E. Minchev -- Boundary Value Problems on Infinite Intervals / J. V. Baxley -- Existence of Steady-State Solutions to Some Constant-Voltage Problems / L. E. Bobisud -- An Existence Theorem for Hereditary Lagrange Problems on an Unbounded Interval / D. A. Carlson -- Dynamical Spectrum for Skew Product Flow in Banach Spaces / S. N. Chow and H. Leiva -- On Boundary Value Problems for First Order Impulse Functional Differential Equations / A. Domoshnitsky and M. Drakhlin -- Linearized Problems and Continuous Dependence / J. A. Ehme