  We present a systematic topological classification of fermionic and bosonic
topological phases protected by time-reversal, particle-hole, parity, and
combination of these symmetries. We use two complementary approaches: one in
terms of K-theory classification of gapped quadratic fermion theories with
symmetries, and the other in terms of the K-matrix theory description of the
edge theory of (2+1)-dimensional bulk theories. The first approach is specific
to free fermion theories in general spatial dimensions while the second
approach is limited to two spatial dimensions but incorporates effects of
interactions. We also clarify the role of CPT theorem in classification of
symmetry-protected topological phases, and show, in particular, topological
superconductors dis- cussed before are related by CPT theorem.
