Abstract We formulate a regular approach for ab initio calculations of the band structure, ground state properties (T=0 K) and excitations ( T≠0) which goes beyond the local-density approximation (LDA) for systems with d- and f-electrons. A diagram technique for non-zero temperature both from the itinerant and atomic limits is developed within a non-orthogonal basis which is generated by the calculation in LDA. LDA is taken as a reference point. Local electron correlations are taken into account by exact transformation of total Hamiltonian to many-electron representation. The derived system of equations for Green's functions of coupled conduction and correlated electrons (including angular momenta, etc.) is presented in closed functional form which allows to construct accurately self-consistent approximations. The approach can be used also in particular cases of any non-commutative algebras, like different spin models with strong anisotropy, or models of correlated electrons (Hubbard, Anderson) for multiple on-site orbitals.