Computational methods are desired for single-cell-resolution spatial transcriptomics (ST) data analysis to uncover spatial organization principles for how individual cells exert tissue-specific functions. Here, we present ST data analysis via interaction-aware cell embedding (SPACE), a deep-learning method for cell-type identification and tissue module discovery from single-cell-resolution ST data by learning a cell representation that captures its gene expression profile and interactions with its spatial neighbors. SPACE identified spatially informed cell subtypes defined by their special spatial distribution patterns and distinct proximal-interacting cell types. SPACE also automatically discovered "cell communities"-tissue modules with discernible boundaries and a uniform spatial distribution of constituent cell types. For each cell community, SPACE outputs a characteristic proximal cell-cell interaction network associated with physiological processes, which can be used to refine ligand-receptor-based intercellular signaling analyses. We envision that SPACE can be used in large-scale ST projects to understand how proximal cell-cell interactions contribute to emergent biological functions within cell communities. A record of this paper's transparent peer review process is included in the supplemental information.