This paper introduces a framework for domain generalization, called Multi-TCA (Multi-Domain Transfer Component Analysis). Domain generalization addresses the question of how to use the knowledge acquired from related domains on new domains. Multi-TCA is based on Transfer Component Analysis (TCA) which is a popular transfer learning technique. TCA learns a shared subspace by minimizing the dissimilarities across domains, while maximally preserving the data variance. We introduce Multi-TCA which is an extension of TCA to multiple domains as well as Multi-SSTCA, which is an extension of TCA for semi-supervised learning. Multi-TCA and Multi-SSTCA are evaluated and compared with other state-of-the-art methods on real and simulated data. Experimental results demonstrate that Multi--TCA can improve predictive performance on previously unseen domains.