These notes deal with certain aspects of the theory of holomorphic functions of several complex variables which have not yet attracted much attention although they are very closely related to classical analysis. Briefly, the object is to see how much of our extremely detailed knowledge about holomorphic functions in the unit disc (such as boundary values, distribution of zeros as related to growth restrictions, factorization theorems, invariant subspaces, interpolation theorems) can be carried over to an analogous situation in several variables, namely to polydiscs. It turns out that one finds some analogues and many counter examples (as is to be expected) but also some genuinely new theorems whose one-variable versions either make no sense or reduce to trivialities. These differences are of course of much greater interest than the similarities.