Alzheimer’s disease (AD) is considered one of the challenges facing health care in the modern century; until now, there has been no effective treatment to cure it, but there are drugs to slow its progression. Therefore, early detection of Alzheimer’s is vital to take needful measures before it develops into brain damage which cannot be treated. Magnetic resonance imaging (MRI) techniques have contributed to the diagnosis and prediction of its progression. MRI images require highly experienced doctors and radiologists, and the analysis of MRI images takes time to analyze each slice. Thus, deep learning techniques play a vital role in analyzing a huge amount of MRI images with high accuracy to detect Alzheimer’s and predict its progression. Because of the similarities in the characteristics of the early stages of Alzheimer’s, this study aimed to extract the features in several methods and integrate the features extracted from more than one method into the same features matrix. This study contributed to the development of three methodologies, each with two systems, with all systems aimed at achieving satisfactory accuracy for the detection of AD and predicting the stages of its progression. The first methodology is by Feed Forward Neural Network (FFNN) with the features of GoogLeNet and DenseNet-121 models separately. The second methodology is by FFNN network with combined features between GoogLeNet and Dense-121 models before and after high-dimensionality reduction of features using the Principal Component Analysis (PCA) algorithm. The third methodology is by FFNN network with combined features between GoogLeNet and Dense-121 models separately and features extracted by Discrete Wavelet Transform (DWT), Local Binary Pattern (LBP) and Gray Level Co-occurrence Matrix (GLCM) methods called handcrafted features. All systems yielded super results in detecting AD and predicting the stages of its progression. With the combined features of the DenseNet-121 and handcrafted, the FFNN achieved an accuracy of 99.7%, sensitivity of 99.64%, AUC of 99.56%, precision of 99.63%, and a specificity of 99.67%.