This text discusses the behavior of acoustic-gravity waves and shock waves in the solar atmosphere, as well as their nonlinear characteristics and the formation of shocks in fluid dynamics. Acoustic-gravity waves experience minimal refraction due to the small variation of sound speed with height, while gravity waves show significant refraction due to changes in the frequency of the wave. As wave amplitude increases, the simple adiabatic model breaks down, leading to nonlinear effects. In an acoustic disturbance, compression waves overtake rarefaction waves, leading to a steepening of the wave profile and the formation of a shock. Shocks move supersonically and can persist as distinct entities in the flow until they are damped by dissipative mechanisms. Unlike acoustic waves, internal gravity waves do not form shocks but instead break into turbulence. Shock waves are important in astrophysics, as they can dissipate energy and heat the surrounding atmosphere. In pulsating stars, strong shocks can alter the thermodynamic and dynamical state of the atmosphere and produce spectroscopic phenomena. In supernova explosions, extremely strong shocks can blow away the outer envelope of a star. Laboratory experiments also show similar shock phenomena, such as in supersonic flows or shock tubes. The development of shocks is analyzed using nonlinear hydrodynamical equations, leading to the concept of simple waves and shock waves. The general solution of these equations shows that physical properties propagate in the same manner as the fluid velocity. For a perfect gas, the relationships between upstream and downstream variables are derived, showing that the upstream flow is supersonic and the downstream flow is subsonic across a shock. The entropy increases across a shock, indicating irreversible dissipation of energy. In steady shocks, the conservation laws are applied to derive jump relations, showing that the entropy increases across the shock. For a perfect gas, the relationships between upstream and downstream variables are expressed in terms of the upstream Mach number. The entropy jump across a shock is determined by the shock strength and is always positive. In relativistic shocks, the jump conditions are generalized, showing that the entropy increases and the shock structure is determined by relativistic effects. Viscous and conducting shocks are analyzed, showing how dissipation processes affect the structure and thickness of the shock front. Viscous shocks lead to an irreversible conversion of kinetic energy into heat, while conducting shocks involve heat transfer and can have different structures compared to purely viscous shocks. The thickness of a shock is related to the mean free path of particles and the pressure jump across the shock. The analysis shows that shocks are thin transition layers where dissipative mechanisms play a key role in determining their structure and behavior.This text discusses the behavior of acoustic-gravity waves and shock waves in the solar atmosphere, as well as their nonlinear characteristics and the formation of shocks in fluid dynamics. Acoustic-gravity waves experience minimal refraction due to the small variation of sound speed with height, while gravity waves show significant refraction due to changes in the frequency of the wave. As wave amplitude increases, the simple adiabatic model breaks down, leading to nonlinear effects. In an acoustic disturbance, compression waves overtake rarefaction waves, leading to a steepening of the wave profile and the formation of a shock. Shocks move supersonically and can persist as distinct entities in the flow until they are damped by dissipative mechanisms. Unlike acoustic waves, internal gravity waves do not form shocks but instead break into turbulence. Shock waves are important in astrophysics, as they can dissipate energy and heat the surrounding atmosphere. In pulsating stars, strong shocks can alter the thermodynamic and dynamical state of the atmosphere and produce spectroscopic phenomena. In supernova explosions, extremely strong shocks can blow away the outer envelope of a star. Laboratory experiments also show similar shock phenomena, such as in supersonic flows or shock tubes. The development of shocks is analyzed using nonlinear hydrodynamical equations, leading to the concept of simple waves and shock waves. The general solution of these equations shows that physical properties propagate in the same manner as the fluid velocity. For a perfect gas, the relationships between upstream and downstream variables are derived, showing that the upstream flow is supersonic and the downstream flow is subsonic across a shock. The entropy increases across a shock, indicating irreversible dissipation of energy. In steady shocks, the conservation laws are applied to derive jump relations, showing that the entropy increases across the shock. For a perfect gas, the relationships between upstream and downstream variables are expressed in terms of the upstream Mach number. The entropy jump across a shock is determined by the shock strength and is always positive. In relativistic shocks, the jump conditions are generalized, showing that the entropy increases and the shock structure is determined by relativistic effects. Viscous and conducting shocks are analyzed, showing how dissipation processes affect the structure and thickness of the shock front. Viscous shocks lead to an irreversible conversion of kinetic energy into heat, while conducting shocks involve heat transfer and can have different structures compared to purely viscous shocks. The thickness of a shock is related to the mean free path of particles and the pressure jump across the shock. The analysis shows that shocks are thin transition layers where dissipative mechanisms play a key role in determining their structure and behavior.