The chapter discusses the theoretical treatment of surface friction between fluids or gases and a solid wall, focusing on the challenges that arise when both viscosity and inertia play significant roles. Two major advancements in this field have been made: L. Prandtl's "Boundary Layer Theory" and H. Blasius' empirical findings on the lawfulness of friction loss in smooth pipes. Prandtl's theory, while providing valuable insights, has limitations due to its mathematical complexity and the narrow range of applicability similar to that of pure streamline flow in pipes. This theory is replaced by a turbulent boundary layer, which is more applicable in practical scenarios. The author then delves into the theory of laminar friction, presenting a simplified approach to Prandtl's boundary layer theory and methods to approximate complex cases using simple mathematical tools. The chapter also explores the calculation of turbulent friction, aiming to apply empirical laws of turbulent pipe resistance to other friction problems. The discussion includes the mathematical formulation of the boundary layer theory, the impulse equation, and the application of these theories to various practical scenarios, such as the friction resistance of a plate moving through a fluid and the turbulent flow in smooth pipes. The author derives empirical formulas for friction resistance and compares them with experimental results, showing good agreement. Finally, the chapter examines the turbulent boundary layer on a flat plate and the laminar friction on a rotating disk, providing detailed mathematical derivations and numerical solutions. The results are validated through comparisons with experimental data, demonstrating the accuracy and applicability of the derived models.The chapter discusses the theoretical treatment of surface friction between fluids or gases and a solid wall, focusing on the challenges that arise when both viscosity and inertia play significant roles. Two major advancements in this field have been made: L. Prandtl's "Boundary Layer Theory" and H. Blasius' empirical findings on the lawfulness of friction loss in smooth pipes. Prandtl's theory, while providing valuable insights, has limitations due to its mathematical complexity and the narrow range of applicability similar to that of pure streamline flow in pipes. This theory is replaced by a turbulent boundary layer, which is more applicable in practical scenarios. The author then delves into the theory of laminar friction, presenting a simplified approach to Prandtl's boundary layer theory and methods to approximate complex cases using simple mathematical tools. The chapter also explores the calculation of turbulent friction, aiming to apply empirical laws of turbulent pipe resistance to other friction problems. The discussion includes the mathematical formulation of the boundary layer theory, the impulse equation, and the application of these theories to various practical scenarios, such as the friction resistance of a plate moving through a fluid and the turbulent flow in smooth pipes. The author derives empirical formulas for friction resistance and compares them with experimental results, showing good agreement. Finally, the chapter examines the turbulent boundary layer on a flat plate and the laminar friction on a rotating disk, providing detailed mathematical derivations and numerical solutions. The results are validated through comparisons with experimental data, demonstrating the accuracy and applicability of the derived models.