In the last year’s topological insulators (TI) have become one of the hottest topics in condensed matter physics. They are defined as insulator electronic phase, which has an energy gap topologically non-equivalent to the vacuum ones. The most robust observable consequence of a nontrivial topological character of the electronic band structure of these materials is the presence of gapless helical surface (edge for 2D TI) states, whose gapless states are protected by time-reversal or crystalline symmetries, and are thus robust to perturbations that do not break this symmetry. Potential applications of TIs for a wide range of devices working at room temper- ature require a large bulk-band gap, but the gap value reported to date is ∼0.35 eV at most.Thus for realizing novel topological phenomena and device applications of TIs, we need new approach to the manipulation of materials properties of TIs.Very suitable approach is the heterostructure engineering where one can alter the stacking sequence of layers or insert different building blocks into the crystal, which may trigger gigantic quantum effects and/or new physical phenomena. In this paper the generation and spectrum of interface topological electron states in the different layered heterostructures structure formed by topological and band insulator are considered. The electronic states of TI and band insulator in three-dimension are described by effective lowenergy kp Hamiltonian of the Dirac like two-band symmetric model     formula     (1) whereM0, A1, A2, B1, and B2 are material parameters, in particular Mo= Eg/2, Eg is the band gap, V is the potential work function. The wave number k in x, y and z directions are denoted by kx, ky and kz, respectively. The matrices σ are two-dimensional unitary and Pauli matrices. The Hamiltonians includes also the terms of intreband mixing by sublatice displacement u. Using coordinate transformation the anisotropy in the off –diagonal terms can be eliminated and below we will consider A1=A2. The analysis of topological electronic states in the layred heterostructures is based on applying the methods of supersymmetry and factorization to solution of the Dirac-type equation (1) with inhomogeneous external potentials    formula    and u (z). For layered heterostructures the Hamiltonians (1) commutes with the chirality operator   formula      (where γ 0 ,γ = (γ 1,γ 2 ,γ 3 ) are the Dirac matrices) as well as with in plane spin operator Σ the Dirac like equation becomes     formula     (2) After quadration (self-produce) the diagonalization of Hamiltonians (2) is possible only in the case when the space variation of potentials V(z), M(z) and u (z) are described by the same function f(z), for example f(z) =th(z/L).Such procedure allows to analyze different layered heterostructures of TI and conventional band insulator, which are characterized by at least one zero-mode in the case of abrupt heterojunction ( L →0) and a lot of interface modes for graded transition region (finite value of L). The TI interface states driven by the electrical polarization fields (terms u in eq.(2)) are identified.Such type of electronic states are analized in different type of heterostructures based on semimetalic and narrow-gap semiconductors Bi1-xSbx, Pb1-xSnxTe, Bi2Te3, HgTe, TlBiTe2 etc. the first part of the paper as well as some old observed properties of materials with band inversion.