The Amyloid-β (Aβ) peptide is one of the main aggregate species in Alzheimer's disease. It is believed that the aggregation of Aβ is crucial to neurotoxicity, which is a hallmark of the disease. While it is clear that Aβ plays a significant role in the deterioration of neurons during the progression of this disease, both the toxic nature of Aβ and the initiation of Aβ aggregation are not well understood. It has been observed that cell membranes, in particular anionic lipids, play a key role in accelerating Aβ aggregation in vivo. Interactions with anionic lipids promote secondary structure changes and a much higher rate of protein aggregation. However, it is unclear how interactions with cell membranes influence the earliest stages of aggregation, which are unavailable to the current resolution of experimental techniques. In this thesis, we present extensive molecular dynamics simulations performed to investigate the direct interaction between Aβ and anionic lipids in order to explain the origin of the substantial influence of cell membranes on Aβ aggregation. From these molecular dynamics simulations, we have observed that anionic cell membranes likely promote aggregation through transiently increasing the local Aβ concentration by favorable protein-lipid interactions on the membrane surface. Further, we have determined that membranes do not directly influence Aβ structure on a monomer level, but the secondary structure change observed in experiments is likely due to protein-protein interactions which are promoted on the membrane surface. Finally, we have determined that anionic lipids act as a catalyst for Aβ dimerization while uncharged lipids likely limit aggregation to only the dimer level. Through these molecular dynamics simulations, we have been able to obtain extensive data on Aβ-membrane interactions at a molecular level. Data such as this will be necessary towards developing a cure to halt Alzheimer's disease progression at its earliest stages.