In this chapter, the kinematics of homogeneous and isotropic turbulence is presented in Sects. 4.1 and 4.2. In Sect. 4.3, the transformation of the differential model into Fourier Space is presented in detail, which resulted in a powerful tool for the physical interpretation of the nonlinearities of turbulent flows. In Sect. 4.4, the concept of Spectral tensor and Turbulent kinetic energy spectrum is presented, whose balance equation is presented in Sect. 4.5. In Sect. 4.6, the Kolmogorov theory is presented, including the characteristic quantities of turbulence, in Sect. 4.7. Finally, a list of exercises is presented in Sect. 4.8.