The past decade in computer vision research has witnessed the re-emergence of "deep learning", and in particular convolutional neural network (CNN) techniques, allowing to learn powerful image feature representations from large collections of examples. CNNs achieve a breakthrough in performance in a wide range of applications such as image classification, segmentation, detection and annotation. Nevertheless, when attempting to apply the CNN paradigm to 3D shapes (feature-based description, similarity, correspondence, retrieval, etc.) one has to face fundamental differences between images and geometric objects. Shape analysis and geometry processing pose new challenges that are non-existent in image analysis, and deep learning methods have only recently started penetrating into our community. The purpose of this tutorial is to overview the foundations and the current state of the art on learning techniques for 3D shape analysis. Special focus will be put on deep learning techniques (CNN) applied to Euclidean and non-Euclidean manifolds for tasks of shape classification, retrieval and correspondence. The tutorial will present in a new light the problems of shape analysis and geometry processing, emphasizing the analogies and differences with the classical 2D setting, and showing how to adapt popular learning schemes in order to deal with 3D shapes. The tutorial will assume no particular background, beyond some basic working knowledge that is a common denominator for students and practitioners in vision and graphics. The recording of the second part is available at: video.