The traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. The calculation of spin-angular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) the numerical codes for the calculation of spin-angular coefficients are usually very time consuming; (ii) f-shells are often omitted from programs for matrix element calculations since the tables for their coefficients of fractional parentage are very extensive. The authors assume that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements can be avoided by using this secondly quantized methodology, based on angular momentum theory, on the concept of the irreducible tensorial sets, on a generalized graphical method, on quasispin and on the reduced coefficients of fractional parentage.