<p>Multiple-source domain adaptation (MDA), aims at transferring knowledge from several source domains to a little or no labeled target domain, has been widely and successfully applied in many fields of machine learning and image processing. Although many MDA algorithms have been proposed in recent years, there have been few theoretical research results. In this paper, we dedicate to studying theory and algorithm for MDA. We provide a theoretical analysis framework for multiple-source domain adaptation based on covering numbers in statistical learning theory. Under this framework, we comprehensively analyze the generalization error bounds of multiple-source domain adaptation in various situations, e.g. unsupervised MDA and semi-supervised MDA. Due to the large number of parameters involved, we also provide an efficient method for selecting parameters based on the derived generalization error bounds. Experimental results confirmed the effectiveness of the proposed method. Furthermore, we propose an adversarial multiple feature spaces adaptation network(AMFSAN) for MDA according to the theoretical results. Numerical simulations indicate that the proposed algorithm is superior to other existing algorithms.</p>