Alzheimer’s disease effects human brain cells and results in dementia. The gradual deterioration of the brain cells results in disability of performing daily routine tasks. The treatment for this disease is still not mature enough. However, its early diagnosis may allow restraining the spread of disease. For early detection of Alzheimer’s through brain Magnetic Resonance Imaging (MRI), an automated detection and classification system needs to be developed that can detect and classify the subject having dementia. These systems also need not only to classify dementia patients but to also identify the four progressing stages of dementia. The proposed system works on an efficient technique of utilizing transfer learning to classify the images by fine-tuning a pre-trained convolutional network, AlexNet. The architecture is trained and tested over the pre-processed segmented (Grey Matter, White Matter, and Cerebral Spinal Fluid) and un-segmented images for both binary and multi-class classification. The performance of the proposed system is evaluated over Open Access Series of Imaging Studies (OASIS) dataset. The algorithm showed promising results by giving the best overall accuracy of 92.85% for multi-class classification of un-segmented images.