  Topological crystalline insulators (TCI) are new topological phases of matter
protected by crystal symmetry of solids. Recently, the first realization of TCI
has been predicted and observed in IV-VI semiconductor SnTe and related alloys
Pb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation,
we present a unified approach to study topological surface states on various
crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p
Hamiltonian for topological surface states from electronic structure of the
bulk, thereby providing a microscopic understanding of bulk-boundary
correspondence in TCI. Depending on the surface orientation, we find two types
of surface states with qualitatively different properties. In particular, we
predict that (111) surface states consist of four Dirac cones centered at
time-reversal-invariant momenta {\Gamma} and M, while (110) surface states
consist of Dirac cones at non-time-reversal-invariant momenta, similar to
(001). Moreover, both (001) and (110) surface states exhibit a Lifshitz
transition as a function of Fermi energy, which is accompanied by a Van-Hove
singularity in density of states arising from saddle points in the band
structure.
