Contrastive Language-Image Pre-training (CLIP) shows promise in medical image analysis but requires substantial data and computational resources. Due to these restrictions, existing CLIP applications in medical imaging focus mainly on modalities like chest X-rays that have abundant image-report data available, leaving many other important modalities under-explored. Here, we propose the first adaptation of the full CLIP model to mammography, which presents significant challenges due to labeled data scarcity, high-resolution images with small regions of interest, and data imbalance. We first develop a specialized supervision framework for mammography that leverages its multi-view nature. Furthermore, we design a symmetric local alignment module to better focus on detailed features in high-resolution images. Lastly, we incorporate a parameter-efficient fine-tuning approach for large language models pre-trained with medical knowledge to address data limitations. Our multi-view and multi-scale alignment (MaMA) method outperforms state-of-the-art baselines for three different tasks on two large real-world mammography datasets, EMBED and RSNA-Mammo, with only 52% model size compared with the largest baseline.