Early detection of Alzheimer's Disease (AD), a neurological disorder, may help in development of appropriate treatment to slow down the disease's progression. In this chapter, a method is proposed that may assist in diagnosis of AD using T1 weighted MRI brain images. In the proposed method, first-and-second-order-statistical features were extracted from multiple trans-axial brain slices covering hippocampus and amygdala regions, which play a significant role in AD diagnosis. Performance of the proposed approach is compared with the state-of-the-art feature extraction techniques in terms of sensitivity, specificity, and accuracy. The experiment was carried out on two datasets built from publicly available OASIS data, with four well-known classifiers. Experimental results show that the proposed method outperforms all the other existing feature extraction techniques irrespective of the choice of classifier and dataset. In addition, the statistical test demonstrates that the proposed method is significantly better in comparison to the existing methods. The authors believe that this study will assist clinicians/researchers in classification of AD patients from controls based on T1-weighted MRI.