As more and more exoplanets are discovered, searching for biosignature gases is becoming one of the crucial ways to find extraterrestrial life. Biosignature gases are gases produced by living organisms that can accumulate to detectable levels in the atmosphere. Once detected, it can be attributed to signs of life on the planet. So far, only a few molecules have been studied as potential biosignature gases. A recent paper proposes that we should systematically evaluate All Small Molecules (ASM) as possible biosignature gases. This thesis summarizes my work in identifying and studying three new potential biosignature gases in terrestrial exoplanet atmospheres. In my research, I use various approaches, from simple Henry's law to our comprehensive photochemistry code and transmission spectra model, to study the biosignature potential of ammonia (NH₃) and methanol (CH₃OH). I also developed a simplified chloride steady-state chemical model to examine whether hydrogen chloride (HCl) is a good bioindicator in an H₂-dominated atmosphere. First, we find that NH₃ in a terrestrial planet's atmosphere is generally a good biosignature gas, primarily because terrestrial planets have no significant known abiotic NH₃ source. NH₃ can accumulate in the atmosphere only if life is a net source of NH₃ and produces enough NH₃ to saturate the surface sinks. Second, we consider CH₃OH a poor biosignature gas in terrestrial exoplanet atmospheres due to the enormous production flux required to reach its detection limit. Although CH₃OH can theoretically accumulate on exoplanets with CO₂- or N₂-dominated atmospheres, such planets' small atmospheric scale height and weak atmosphere signals put them out of reach for near-term observations. Finally, albeit HCl has many advantages of being a potential bioindicator, we find it is not a suitable bioindicator because it cannot accumulate to detectable levels on an exoplanet with an H₂-dominated atmosphere orbiting an M5V dwarf star. The extremely high water solubility of HCl means that wet deposition can efficiently remove it from the atmosphere, preventing HCl from accumulating to detectable levels in the atmosphere. Overall, my thesis aims to improve our understanding of biosignature gases and provide more diverse research methods and a more comprehensive framework for future work.Ph.D.