Cross-domain recommendation is an important method to improve recommender system performance, especially when observations in target domains are sparse. However, most existing techniques focus on single-target or dual-target cross-domain recommendation (CDR) and are hard to be generalized to CDR with multiple target domains. In addition, the negative transfer problem is prevalent in CDR, where the recommendation performance in a target domain may not always be enhanced by knowledge learned from a source domain, especially when the source domain has sparse data. In this study, we propose CAT-ART, a multi-target CDR method that learns to improve recommendations in all participating domains through representation learning and embedding transfer. Our method consists of two parts: a self-supervised Contrastive AuToencoder (CAT) framework to generate global user embeddings based on information from all participating domains, and an Attention-based Representation Transfer (ART) framework which transfers domain-specific user embeddings from other domains to assist with target domain recommendation. CAT-ART boosts the recommendation performance in any target domain through the combined use of the learned global user representation and knowledge transferred from other domains, in addition to the original user embedding in the target domain. We conducted extensive experiments on a collected real-world CDR dataset spanning 5 domains and involving a million users. Experimental results demonstrate the superiority of the proposed method over a range of prior arts. We further conducted ablation studies to verify the effectiveness of the proposed components. Our collected dataset will be open-sourced to facilitate future research in the field of multi-domain recommender systems and user modelling.