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This paper addresses classification tasks on a particular target domain in which labeled training data are only available from source domains different from (but related to) the target. Two closely related frameworks, domain adaptation and domain generalization, are concerned with such tasks, where the only difference between those frameworks is the availability of the unlabeled target data: domain adaptation can leverage unlabeled target information, while domain generalization cannot. We propose Scatter Component Analyis (SCA), a fast representation learning algorithm that can be applied to both domain adaptation and domain generalization. SCA is based on a simple geometrical measure, i.e., scatter, which operates on reproducing kernel Hilbert space. SCA finds a representation that trades between maximizing the separability of classes, minimizing the mismatch between domains, and maximizing the separability of data; each of which is quantified through scatter. The optimization problem of SCA can be reduced to a generalized eigenvalue problem, which results in a fast and exact solution. Comprehensive experiments on benchmark cross-domain object recognition datasets verify that SCA performs much faster than several state-of-the-art algorithms and also provides state-of-the-art classification accuracy in both domain adaptation and domain generalization. We also show that scatter can be used to establish a theoretical generalization bound in the case of domain adaptation.