Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from  previous learning tasks to improve the performance of new ones. In this talk, we will first present transfer learning in the early diagnosis of eye diseases: diabetic retinopathy and retinopathy of prematurity.  We will discuss how this empirical  study leads to the mathematical analysis of the feasibility issue in transfer learning, for which we build for the first time, to the best of our knowledge, a mathematical framework for the general procedure of transfer learning. Within this framework,  we establish  the feasibility of transfer learning by showing its  equivalence to the well-definedness of an associated optimization problem.