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Time-series data, which represent the evolution of one or more variables over time, are ubiquitous across domains such as finance, medicine, industry, and security. Time-Series Anomaly Detection (TSAD) is essential for identifying irregular events such as equipment failures, fraudulent activities, and neurological disorders. Despite significant progress, TSAD remains challenging due to the complexity of time-series signals, the diversity of anomaly types, and the scarcity of high-quality labeled data. This thesis contributes: (i) the first comprehensive surveys of Graph-based TSAD (G-TSAD) and Self-Supervised Learning for Anomaly Detection (SSL-AD), showing how graph modeling and SSL proxy tasks yield robust representations for TSAD while mapping limits and future directions; (ii) EEG-CGS, a contrastive–generative SSL framework that encodes fine-grained subgraph structure without anomaly labels, improving multivariate TSAD and localizing anomalous sensors and regions; (iii) TSAD-C, which integrates graph representations with diffusion models to capture long-range temporal and spatial dependencies while explicitly handling contaminated training data; and (iv) extending TSAD beyond benchmark datasets into other impactful domains, and developing foundation models specialized for biosignals to detect novel anomalies in drug-resistant epilepsy patients.