Deep neural networks can be trained to create highly accurate image classification models, provided we have access to large datasets. In few-shot learning, data is limited to few images, so training from scratch is not feasible. First, a task-independent representation function is learned on abundant data by solving a distinct task such as multiclass classification on a set of base classes. Then, the learned representation is combined with new data of novel classes to solve the few-shot task. In both stages, we introduce solutions that aim at leveraging available data as much as possible. In particular, for representation learning, we propose dense classification training, which for the first time studies local activations in the domain of few-shot learning. We also propose two solutions to adapt the representation function to the few-shot task. Learning is limited to few parameters in implanting or to few gradient updates. Additionally, we study alternative few-shot learning settings, in which access to data is modified. In transductive learning, multiple images need to be classified at the same time. In this context, we propose local propagation, a method that uses similarities between local representations of images to propagate class information. We also introduce few-shot few-shot learning, a new setting, where only few or no in-domain data is accessible for representation learning. In this context, we take advantage of a classifier, pre-trained on a large-scale dataset of a different domain, which can still be adapted to the domain if data is available. In few-shot learning, because data is so scarce, we show that selecting relevant regions with an attention mechanism is important. We propose two simple solutions that successfully fulfill this role. Finally, we apply our knowledge of few-shot learning on the specific problem of classifying aerial images.