This chapter introduces the concept of turbulence, focusing on homogeneous and isotropic fluid turbulence. Turbulence is characterized by two main properties: a quasi-constant flux of energy from large to small scales (direct cascade) and systematic randomness that requires a statistical description. The chapter uses shock formation as a simplified model to illustrate these properties. Numerical solutions of the 1D compressible Navier-Stokes equations are presented to show how an initially smooth profile evolves into a shock with a steep gradient. The evolution of harmonics, energy spectra, and kinetic energy over time is discussed, highlighting the nonlinear advection term's role in distributing energy across different wave numbers. The shock formation process is seen as a deterministic version of "turbulent dissipation," where energy is distributed among various scales, including the dissipation scales where viscosity becomes significant.This chapter introduces the concept of turbulence, focusing on homogeneous and isotropic fluid turbulence. Turbulence is characterized by two main properties: a quasi-constant flux of energy from large to small scales (direct cascade) and systematic randomness that requires a statistical description. The chapter uses shock formation as a simplified model to illustrate these properties. Numerical solutions of the 1D compressible Navier-Stokes equations are presented to show how an initially smooth profile evolves into a shock with a steep gradient. The evolution of harmonics, energy spectra, and kinetic energy over time is discussed, highlighting the nonlinear advection term's role in distributing energy across different wave numbers. The shock formation process is seen as a deterministic version of "turbulent dissipation," where energy is distributed among various scales, including the dissipation scales where viscosity becomes significant.