Breast cancer remains one of the leading causes of mortality among women worldwide, making early and accurate detection through mammography essential for improving patient outcomes. In recent years, Convolutional Neural Networks (CNNs) have demonstrated strong performance in automated mammogram classification tasks. However, their effectiveness is often limited to the datasets on which they are trained, as variations in imaging devices, acquisition protocols, and patient demographics introduce significant domain shift. This results in reduced performance when models are applied to unseen datasets, posing a major challenge for real-world clinical deployment. This study addresses the problem of cross-dataset generalization in CNN-based mammogram classification by incorporating domain adaptation techniques. A hybrid domain adaptation framework is proposed, integrating feature-level alignment, adversarial learning, and batch normalisation adaptation to reduce the distribution discrepancy between source and target domains. The model is trained using labelled data from a source dataset and unlabeled data from a target dataset to learn domain-invariant feature representations. Experimental evaluations conducted on multiple publicly available mammography datasets, including DDSM, MIAS, and INbreast, demonstrate that the proposed approach significantly improves classification performance across different domains. The results show notable gains in accuracy and Area Under the Curve (AUC) compared to baseline CNN models without domain adaptation. The findings emphasise the importance of domain adaptation in enhancing the robustness and generalizability of deep learning models for medical imaging, supporting the development of reliable and scalable computer-aided diagnosis systems for breast cancer detection.