  In this paper we systematically classify and describe bosonic symmetry
protected topological (SPT) phases in all physical spatial dimensions using
semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases
on a $d-$dimensional lattice discussed in this paper can be described by the
same NLSM, which is an O(d+2) NLSM in $(d+1)-$dimensional space-time, with a
topological $\Theta-$term. The field in the NLSM is a semiclassical Landau
order parameter with a unit length constraint. The classification of SPT phases
discussed in this paper based on their NLSMs is consistent with the more
mathematical classification based on group cohomology. Besides the
classification, the formalism used in this paper also allows us to explicitly
discuss the physics at the boundary of the SPT phases, and it reveals the
relation between SPT phases with different symmetries. For example, it gives
many of these SPT states a natural "decorated defect" construction.
