Gamma-ray emission can be generated from a wide variety of high-energy astrophysical phenomena, from stellar flares to pulsating neutron stars, and from interstellar clouds to the center of the Milky Way Galaxy. Entering the 13th year of its orbit around Earth, the Fermi Space Gamma-ray Telescope has been continually surveying the gamma-ray sky with its Large Area Telescope (LAT) on board. The latest Fermi source catalog contains almost 6000 sources. Yet, a lot of sources that are expected to emit gamma-rays are not detected, and only small percentages of some populations are detected. For example, solar flares are detected in gamma-rays, do other stellar flares also produce gamma-ray photons? Only 10% of pulsars discovered to date are detected in gamma-rays, do the remaining 90% emit gamma-rays too?
This work aims to provide a novel technique to analyze Fermi-LAT data as we approach the point source sensitivity limit of the instrument. Detecting and characterizing gamma-ray emission from these underlying populations is important for understanding the physical processes associated with these sources. Stacking methods are used to uncover as much information as possible about populations of sources hidden in the noise, and to study the origins of the high-energy emission. In this thesis, the proposed methods are applied to varied sources such as flare stars, pulsars, globular clusters, and low-mass X-ray binaries. I will discuss general properties of the overall population, and their emission mechanisms, such as stellar auroral phenomena, inverse Compton scattering, particle acceleration, etc.