and summary -- Multiplication theorems and square theorems; Bourlet operators -- Substitution operators. The Schröder equation -- Continuous iteration. Commuting substitution operators -- Relations beiween Bourlet operators of the specific form -- Superposition of substitution operators -- Integral operators: Remarks and definitions -- The theorems of Weyl and von Neumann on hermitean Carleman operators -- Recent results on Carleman operators -- Strong Carleman operators -- Convergence theorems -- Transformation of strong Kernels -- Operators of locally bounded range -- Concluding remakrs. Open questions.