This thesis investigates the formation of the Martian moons, Phobos and Deimos, through detailed simulations of Giant Impacts, the leading hypothesis for their origin. Phobos and Deimos, characterized by their small size, irregular shape, and near-equatorial, near-circular orbits, pose challenges for alternative formation theories, such as asteroid capture. The Giant Impact hypothesis, however, suggests that the moons formed from a debris disk created by the collision of Mars with an impactor of comparable size. This study aims to refine our understanding of such disk-forming collisions by employing a novel impact code, using Smoothed Particle Hydrodynamics (SPH), to simulate a range of impact scenarios. Key variables, including the mass ratio between the impactor and Mars, impact velocities, and collision angles, are systematically explored to determine their effects on the formation, composition, and stability of the resulting debris disk. Particular emphasis is placed on evaluating the role of material strength, a factor often neglected in large-scale planetary collision models. By comparing simulations that account for material strength with those that treat the colliding bodies as purely fluid, this work examines how material properties influence the dynamics of the impact, disk formation, and subsequent evolution. The results reveal how specific impact conditions affect the distribution of material within the disk, including contributions from Mars and the impactor. Additionally, the thesis investigates the evolution of disk mass, angular momentum profiles, and stability over time, providing critical insights into the physical processes prior to the moon formation. These findings also serve as theoretical predictions that can be tested against upcoming data from the Martian Moons eXploration (MMX) mission, which will return samples from Phobos. Ultimately, this research enhances our understanding of the origins of Phobos and Deimos and contributes to the broader field of planetary science by shedding light on the role of giant impacts in shaping planetary systems.