Transfer Learning is a well-studied concept in machine learning, that relaxes the assumption that training and testing data need to be drawn from the same distribution. Recent success in applying transfer learning in the area of computer vision has motivated research on transfer learning also in context of time series data. This benefits learning in various time series domains, including a variety of domains based on sensor values. In this paper, we conduct a systematic mapping study of literature on transfer learning with time series data. Following the review guidelines of Kitchenham and Charters, we identify and analyze 223 relevant publications. We describe the pursued approaches and point out trends. Especially during the last two years, there has been a vast increase in the number of publications on the topic. This paper's findings can help researchers as well as practitioners getting into the field and can help identify research gaps.