Alzheimer's disease is the most common form of dementia and is a serious health problem. The disease is expected to increase further in the upcoming years with the increase of the elderly population. Developing new treatments and diagnostic methods is getting more important. In this study, we focused on the early diagnosis of dementia in Alzheimer's disease via analysis of neuroimages. We analyzed the data diagnosed by the Alzheimer's Disease Neuroimaging Initiative (ADNI) protocol. The analyzed data were T1-weighted magnetic resonance images of 159 patients with Alzheimer's disease, 217 patients with mild cognitive impairment and 109 cognitively healthy older people. In this study, we propose that the volumetric reduction in the hippocampus is the most important indicator of Alzheimer's disease. There is not much research about the relationship between the volumetric reduction in the hippocampus and Alzheimer's disease. This volume information was calculated through semi-automatic segmentation software ITK-SNAP and a data set was created based on age, gender, diagnosis, and right and left hippocampal volume values. The diagnosis via hippocampal volume information was made by using machine learning techniques. By using this approach, we conclude that brain MRIs can be used to distinguish the patients with Alzheimer's Disease (AD), Mild Cognitive Impairment (MCI) and Cognitive Normal (CN) from each other; while most of the studies were only able to distinguish AD from CN. Our results have revealed that our approach improves the performance of the computer-aided diagnosis of Alzheimer's disease.