  Most superconducting materials have an inversion center in their crystal
lattices. One of few exceptions is the recently discovered heavy-fermion
superconductor CePt3Si [E. Bauer et al, Phys. Rev. Lett. 92, 027003 (2004)]. In
this paper, we analyze the implications of the lack of inversion symmetry for
the superconducting pairing. We show that the order parameter is an odd
function of momentum, and that there always are lines of zeros in the
excitation energy gap for one-component order parameters, which seems to agree
with the experimental data. The superconducting phase can be non-uniform, even
without external magnetic field, due to the presence of unusual gradient terms
in the Ginzburg-Landau free energy. Also, we performed ab initio electronic
structure calculations for CePt3Si, which showed that the spin-orbit coupling
in this material is strong, and the degeneracy of the bands is lifted
everywhere except along some high symmetry lines in the Brillouin zone.
