A large class of symmetry-protected topological phases (SPT) in boson / spin
systems have been recently predicted by the group cohomology theory. In this
work, we consider SPT states at least with charge symmetry (U(1) or Z$_N$) or
spin $S^z$ rotation symmetry (U(1) or Z$_N$) in 2D, 3D, and the surface of 3D.
If both are U(1), we apply external electromagnetic field / `spin gauge field'
to study the charge / spin response. For the SPT examples we consider (i.e.
U$_c$(1)$\times$[U$_s$(1)$\rtimes$Z$_2$]; subscripts $c$ and $s$ are short for
charge and spin; Z$^T_2$ and Z$_2$ are time-reversal symmetry and
$\pi$-rotation about $S^y$, respectively), many variants of Witten effect in
the 3D SPT bulk and various versions of anomalous surface quantum Hall effect
are defined and systematically investigated. If charge or spin symmetry reduces
to Z$_N$ by considering charge-$N$ or spin-$N$ condensate, instead of the
linear response approach, we gauge the charge/spin symmetry, leading to a
dynamical gauge theory with some remaining global symmetry. The 3D dynamical
gauge theory describes a symmetry-enriched topological phase (SET), i.e. a
topologically ordered state with global symmetry which admits nontrivial ground
state degeneracy depending on spatial manifold topology. For the SPT examples
we consider, the corresponding SET states are described by dynamical
topological gauge theory with topological BF term and axionic $\Theta$-term in
3D bulk. And the surface of SET is described by the chiral boson theory with