Active galactic nuclei (AGN) in galaxy clusters inject vast amounts of energy into the hot intracluster medium (ICM), preventing gas from cooling and suppressing star formation. High-resolution X-ray observations show that the gas in galaxy clusters does not cool at the expected rates, and X-ray images reveal giant cavities and shock fronts, which are direct indicators of AGN energy injection. These cavities, often associated with radio jets, suggest that AGN feedback is crucial for regulating cooling flows and galaxy growth. The energy required to suppress cooling is substantial, on the order of $10^{62}$ erg, and must be deposited in the ICM to prevent excessive star formation. AGN outbursts can alter large-scale properties of the ICM, influencing the thermal and dynamical state of galaxy clusters. X-ray studies of galaxy clusters reveal that the ICM has temperatures ranging from 10 to 100 million K, with X-ray luminosities up to $10^{45}$ erg s$^{-1}$. The gas is primarily composed of ionized hydrogen and helium, with trace amounts of heavier elements. The ICM is held in place by the gravitational potential of dark matter, and its properties are influenced by both gravitational and non-gravitational heating mechanisms. Magnetic fields in the ICM are relatively weak, but they play a role in modifying transport coefficients such as thermal conduction and viscosity. Cooling flows, where gas cools and condenses onto central galaxies, are a key phenomenon in galaxy clusters. However, observations have shown that the expected cooling rates are not always realized, suggesting that AGN feedback is suppressing cooling. The presence of cavities and shock fronts in the ICM indicates that AGN jets are injecting energy into the gas, counteracting radiative losses and preventing excessive cooling. This feedback mechanism is essential for regulating the growth of luminous galaxies and maintaining the thermal balance of the ICM. The study of radio lobes and cavities in galaxy clusters has provided insights into the energy injection processes and the role of AGN in galaxy evolution. These structures are often associated with powerful radio sources and can span large volumes, creating a "Swiss cheese" topology in the ICM. The energy required to inflate these cavities is enormous, on the order of $10^{55}$ to $10^{61}$ erg, and is primarily supplied by AGN outbursts. The interaction between AGN feedback and the ICM is a critical factor in understanding the evolution of galaxy clusters and the formation of large-scale structures in the universe.Active galactic nuclei (AGN) in galaxy clusters inject vast amounts of energy into the hot intracluster medium (ICM), preventing gas from cooling and suppressing star formation. High-resolution X-ray observations show that the gas in galaxy clusters does not cool at the expected rates, and X-ray images reveal giant cavities and shock fronts, which are direct indicators of AGN energy injection. These cavities, often associated with radio jets, suggest that AGN feedback is crucial for regulating cooling flows and galaxy growth. The energy required to suppress cooling is substantial, on the order of $10^{62}$ erg, and must be deposited in the ICM to prevent excessive star formation. AGN outbursts can alter large-scale properties of the ICM, influencing the thermal and dynamical state of galaxy clusters. X-ray studies of galaxy clusters reveal that the ICM has temperatures ranging from 10 to 100 million K, with X-ray luminosities up to $10^{45}$ erg s$^{-1}$. The gas is primarily composed of ionized hydrogen and helium, with trace amounts of heavier elements. The ICM is held in place by the gravitational potential of dark matter, and its properties are influenced by both gravitational and non-gravitational heating mechanisms. Magnetic fields in the ICM are relatively weak, but they play a role in modifying transport coefficients such as thermal conduction and viscosity. Cooling flows, where gas cools and condenses onto central galaxies, are a key phenomenon in galaxy clusters. However, observations have shown that the expected cooling rates are not always realized, suggesting that AGN feedback is suppressing cooling. The presence of cavities and shock fronts in the ICM indicates that AGN jets are injecting energy into the gas, counteracting radiative losses and preventing excessive cooling. This feedback mechanism is essential for regulating the growth of luminous galaxies and maintaining the thermal balance of the ICM. The study of radio lobes and cavities in galaxy clusters has provided insights into the energy injection processes and the role of AGN in galaxy evolution. These structures are often associated with powerful radio sources and can span large volumes, creating a "Swiss cheese" topology in the ICM. The energy required to inflate these cavities is enormous, on the order of $10^{55}$ to $10^{61}$ erg, and is primarily supplied by AGN outbursts. The interaction between AGN feedback and the ICM is a critical factor in understanding the evolution of galaxy clusters and the formation of large-scale structures in the universe.