This dissertation covers a very actual research topic -- numerical treatment of high-dimensional problems. This research work is a contribution to the theory of information-based complexity (IBC). The first chapter is an introduction and contains abstract problems connected with IBC. In Chapter 2, special classes of numerical problems are described. Especially, the singular value decomposition (SVD) of compact operators between Hilbert spaces is given. It is often connected with optimal algorithms. Tensor product structures in Hilbert spaces are also studied. Some results which concern reproducing kernel Hilbert spaces (RKHSs) are given. In the third chapter, a characterization of the different types of tractability of scaled tensor product problems between Hilbert spaces is received. One of the main results is obtaining the complete characterization for the normalized error criterion and the scaling factors become irrelevant. These new properties are a generalization of the previously known theory. Some examples are given. In Chapter 4, function spaces endowed with weighted norms are explored. The concept of weighted spaces is fully described. An algorithm in an unanchored Sobolev space equipped with product weight that satisfies suitable upper error bounds is obtained. Complexity properties for a whole scale of product-weighted Banach spaces are received. An optimal algorithm for the \(L_{\infty}\)-approximation on an unanchored Sobolev space equipped with product weight is found. (Anti)symmetry conditions are studied in Chapter 5. A generalization of the notation of (anti)symmetry to tensor products of abstract Hilbert spaces is received. (Anti)symmetric numerical problems \(S_{I}\) by the restriction of a given tensor product problem \(S\) to the subspaces of (anti)symmetric elements in the source spaces are formulated. Some applications that demonstrate how important are (anti)symmetry conditions for information complexity. The theory is applied in given examples to the wavefunctions. This dissertation is a contribution to the curse of dimensionality theory and can be used from many researchers in the field of algorithms complexity.