  We show that the fundamental time reversal invariant (TRI) insulator exists
in 4+1 dimensions, where the effective field theory is described by the 4+1
dimensional Chern-Simons theory and the topological properties of the
electronic structure is classified by the second Chern number. These
topological properties are the natural generalizations of the time reversal
breaking (TRB) quantum Hall insulator in 2+1 dimensions. The TRI quantum spin
Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimension
can be obtained as descendants from the fundamental TRI insulator in 4+1
dimensions through a dimensional reduction procedure. The effective topological
field theory, and the $Z_2$ topological classification for the TRI insulators
in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All
physically measurable topological response functions of the TRI insulators are
completely described by the effective topological field theory. Our effective
topological field theory predicts a number of novel and measurable phenomena,
the most striking of which is the topological magneto-electric effect, where an
electric field generates a magnetic field in the same direction, with an
universal constant of proportionality quantized in odd multiples of the fine
structure constant $\alpha=e^2/\hbar c$. Finally, we present a general
classification of all topological insulators in various dimensions, and
describe them in terms of a unified topological Chern-Simons field theory in
phase space.
