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This Third Edition sheds light on state-of-the-art theories and practices in multimodal compatibility modeling and recommendation, offering comprehensive insights into this evolving field. This topic, and fashion compatibility modeling in particular, has garnered increasing research attention in recent years due to the significant economic impact of e-commerce. Building upon recent research and the prior edition, the authors present a series of graph-learning based multimodal compatibility modeling schemes, all of which have been proven to be effective over several public real-world datasets. This book introduces a number of advanced multimodal compatibility modeling and recommendation methods, including category-guided multimodal compatibility modeling and try-on-guided multimodal compatibility modeling. The authors also provide comprehensive solutions, including correlation-oriented graph learning, modality-oriented graph learning, unsupervised disentangled graph learning, partially supervised disentangled graph learning, and metapath-guided heterogeneous graph learning.