The paper discusses the topological properties of time-reversal invariant (TRI) insulators in various dimensions, focusing on the fundamental TRI insulator in 4+1 dimensions. The effective field theory for this insulator is described by a Chern-Simons theory, and its topological properties are classified by the second Chern number. The authors show that the TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimensions can be derived from the fundamental TRI insulator through a dimensional reduction procedure. This procedure naturally leads to the $Z_2$ topological classification for these lower-dimensional insulators. The paper also predicts novel topological effects, such as the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine structure constant. The authors present a general classification of all topological insulators in various dimensions and describe them using a unified topological Chern-Simons field theory in phase space.The paper discusses the topological properties of time-reversal invariant (TRI) insulators in various dimensions, focusing on the fundamental TRI insulator in 4+1 dimensions. The effective field theory for this insulator is described by a Chern-Simons theory, and its topological properties are classified by the second Chern number. The authors show that the TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimensions can be derived from the fundamental TRI insulator through a dimensional reduction procedure. This procedure naturally leads to the $Z_2$ topological classification for these lower-dimensional insulators. The paper also predicts novel topological effects, such as the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine structure constant. The authors present a general classification of all topological insulators in various dimensions and describe them using a unified topological Chern-Simons field theory in phase space.