We introduce a neural method for transfer learning between two (source and target) classification tasks or aspects over the same domain. Rather than training on target labels, we use a few keywords pertaining to source and target aspects indicating sentence relevance instead of document class labels. Documents are encoded by learning to embed and softly select relevant sentences in an aspect-dependent manner. A shared classifier is trained on the source encoded documents and labels, and applied to target encoded documents. We ensure transfer through aspect-adversarial training so that encoded documents are, as sets, aspect-invariant. Experimental results demonstrate that our approach outperforms different baselines and model variants on two datasets, yielding an improvement of 27% on a pathology dataset and 5% on a review dataset.