Sensor-based human activity recognition (HAR) requires to predict the action of a person based on sensor-generated time series data. HAR has attracted major interest in the past few years, thanks to the large number of applications enabled by modern ubiquitous computing devices. While several techniques based on hand-crafted feature engineering have been proposed, the current state-of-the-art is represented by deep learning architectures that automatically obtain high level representations and that use recurrent neural networks (RNNs) to extract temporal dependencies in the input. RNNs have several limitations, in particular in dealing with long-term dependencies. We propose a novel deep learning framework, TrASenD, based on a purely attention-based mechanism, that overcomes the limitations of the state-of-the-art. We show that our proposed attention-based architecture is considerably more powerful than previous approaches, with an average increment, of more than 7% on the F1 score over the previous best performing model. Furthermore, we consider the problem of personalizing HAR deep learning models, which is of great importance in several applications. We propose a simple and effective transfer-learning based strategy to adapt a model to a specific user, providing an average increment of 6% on the F1 score on the predictions for that user. Our extensive experimental evaluation proves the significantly superior capabilities of our proposed framework over the current state-of-the-art and the effectiveness of our user adaptation technique. [ABSTRACT FROM AUTHOR]