This paper presents a topological field theory for time-reversal invariant (TRI) insulators in 4+1 dimensions, where the effective theory is described by the 4+1 dimensional Chern-Simons theory and the topological properties are classified by the second Chern number. These properties generalize 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 dimensions are descendants of the 4+1 dimensional TRI insulator through dimensional reduction. The effective topological field theory and the Z₂ topological classification for TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of TRI insulators are completely described by the effective topological field theory. The paper predicts a novel topological magneto-electric effect, where an electric field generates a magnetic field in the same direction with a quantized proportionality constant. It also presents a general classification of all topological insulators in various dimensions using a unified topological Chern-Simons field theory in phase space. The paper discusses the physical consequences of the second Chern number, the dimensional reduction of TRI insulators to lower dimensions, and the Z₂ classification of TRI insulators in 2+1 and 3+1 dimensions. The paper also provides a detailed analysis of the first Chern number and its relation to the QH effect, the dimensional reduction procedure, and the Z₂ classification of particle-hole symmetric insulators in 1+1 dimensions. The paper concludes with a discussion of the topological properties of TRI insulators and their classification in various dimensions.This paper presents a topological field theory for time-reversal invariant (TRI) insulators in 4+1 dimensions, where the effective theory is described by the 4+1 dimensional Chern-Simons theory and the topological properties are classified by the second Chern number. These properties generalize 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 dimensions are descendants of the 4+1 dimensional TRI insulator through dimensional reduction. The effective topological field theory and the Z₂ topological classification for TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of TRI insulators are completely described by the effective topological field theory. The paper predicts a novel topological magneto-electric effect, where an electric field generates a magnetic field in the same direction with a quantized proportionality constant. It also presents a general classification of all topological insulators in various dimensions using a unified topological Chern-Simons field theory in phase space. The paper discusses the physical consequences of the second Chern number, the dimensional reduction of TRI insulators to lower dimensions, and the Z₂ classification of TRI insulators in 2+1 and 3+1 dimensions. The paper also provides a detailed analysis of the first Chern number and its relation to the QH effect, the dimensional reduction procedure, and the Z₂ classification of particle-hole symmetric insulators in 1+1 dimensions. The paper concludes with a discussion of the topological properties of TRI insulators and their classification in various dimensions.