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Active Galactic Nuclei (AGNs) are the most mystic objects in the universe. They are usually very far away from our Galaxy, which means that they are ancient objects. They are also luminous and have unique features in their spectra. Studying AGNs helps understanding the early universe and the evolution of galaxies. This Dissertation aims to research the structure of AGNs and the cooling function in the AGNs environment. I first investigate what optical/ultraviolet spectroscopic features would be produced by Broad-line Region (BLR) clouds crossing our line of sight to the accretion disk, the source of the optical/UV continuum. This research, prompted by recent X-ray observations, suggests that single cloud has little effect on the optical/UV spectrum. However, an ensemble of clouds produces a strong distinctive feature between the Lyman limit and Lyα. The extent of these features indicates the line-of-sight covering factor of clouds and may explain the ubiquitous AGN spectral break around 1100Å. I next study, considering the physical parameters of AGNs, how the gas cooling function changes at high temperature (T > 104 K) over a wide range of density (nH < 1012 cm−3) and metallicity (Z < 30Z⊙). I find that both density and metallicity change the ionization status of the gas. I provide numerical cooling functions by describing the total cooling as a sum of four parts: that due to H&He, the heavy elements, electron-electron bremsstrahlung, and grains. Finally, I also provide a function giving the electron fraction, which can be used to convert the cooling function into a cooling rate. Last, I extend the cooling-function study to the seldom-explored low-temperature range (T < 104 K). For primordial gas, gas lacking elements heavier than B, I find that radiative attachment and Compton recoil are important cooling processes when the gas kinetic temperature is lower than the temperature of the cosmic microwave background. I also find that collisional de-excitation of HD and H2 is not important above 1000K unlike claims of previous studies. For the dust-free solar case, we identify water as the dominant coolant in high density-environments. We also analyze the parameter ranges where metal, metal molecules, or all molecules, dominate the total cooling. We provide the density, above which the metal or metal molecules become the dominant coolants, as a function of temperature and metallicity. For the ISM case, with dust and depleted abundances, we find that dust does not directly cool the gas. Rather, dust modifies he cooling by affecting the chemistral balance. Similar to the high-temperature case, I also provide numerical cooling data.