In these lecture notes, we provide an overview of some of the high-level research directions and open questions relating to knowledge graphs. We discuss six high-level concepts relating to knowledge graphs: data models, queries, ontologies, rules, embeddings and graph neural networks. While traditionally these concepts have been explored by different communities in the context of graphs, more recent works have begun to look at how they relate to one another, and how they can be unified. In fact, at a more foundational level, we can find some surprising relations between the different concepts. The research questions we explore mostly involve combinations of these concepts.