Electroencephalography (EEG) has emerged as a cost-effective and efficient tool to support neurologists in the detection of Alzheimer's Disease (AD). However, most existing approaches rely heavily on manual feature engineering or data transformation. While such techniques may provide benefits when working with small-scale datasets, they often lead to information loss and distortion when applied to large-scale data, ultimately limiting model performance. Moreover, the limited subject scale and demographic diversity of datasets used in prior studies hinder comprehensive evaluation of model robustness and generalizability, thus restricting their applicability in real-world clinical settings. To address these challenges, we propose ADformer, a novel multi-granularity spatial-temporal transformer designed to capture both temporal and spatial features from raw EEG signals, enabling effective end-to-end representation learning. Our model introduces multi-granularity embedding strategies across both spatial and temporal dimensions, leveraging a two-stage intra-inter granularity self-attention mechanism to learn both local patterns within each granularity and global dependencies across granularities. We evaluate ADformer on 4 large-scale datasets comprising a total of 1,713 subjects, representing one of the largest corpora for EEG-based AD detection to date, under a cross-validated, subject-independent setting. Experimental results demonstrate that ADformer consistently outperforms existing methods, achieving subject-level F1 scores of 92.82%, 89.83%, 67.99%, and 83.98% on the 4 datasets, respectively, in distinguishing AD from healthy control (HC) subjects.