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This paper presents a domain-guided approach for learning representations of scalp-electroencephalograms (EEGs) without relying on expert annotations. Expert labeling of EEGs has proven to be an unscalable process with low inter-reviewer agreement because of the complex and lengthy nature of EEG recordings. Hence, there is a need for machine learning (ML) approaches that can leverage expert domain knowledge without incurring the cost of labor-intensive annotations. Self-supervised learning (SSL) has shown promise in such settings, although existing SSL efforts on EEG data do not fully exploit EEG domain knowledge. Furthermore, it is unclear to what extent SSL models generalize to unseen tasks and datasets. Here we explore whether SSL tasks derived in a domain-guided fashion can learn generalizable EEG representations. Our contributions are three-fold: 1) we propose novel SSL tasks for EEG based on the spatial similarity of brain activity, underlying behavioral states, and age-related differences; 2) we present evidence that an encoder pretrained using the proposed SSL tasks shows strong predictive performance on multiple downstream classifications; and 3) using two large EEG datasets, we show that our encoder generalizes well to multiple EEG datasets during downstream evaluations.