In the past decade, deep learning methods have achieved unprecedented performance on a broad range of problems in various fields from computer vision to speech recognition. However, so far research has mainly focused on developing deep learning methods for Euclidean-structured data. However, many important applications have to deal with non-Euclidean structured data, such as graphs and manifolds. Such geometric data are becoming increasingly important in computer graphics and 3D vision, sensor networks, drug design, biomedicine, recommendation systems, and web applications. The adoption of deep learning in these fields has been lagging behind until recently, primarily since the non-Euclidean nature of objects dealt with makes the very definition of basic operations used in deep networks rather elusive. The purpose of the course is to introduce the emerging field of geometric deep learning on graphs and manifolds, overview existing solutions and applications, as well as key challenges and future directions.