The i* modeling language was introduced to fill the gap in the spectrum of conceptual modeling languages, focusing on the intentional (why?), social (who?), and strategic (how? how else?) dimensions. i* has been applied in many areas, e.g., healthcare, security analysis, eCommerce. Although i* has seen much academic application, the diversity of extensions and variations can make it difficult for novices to learn and use it in a consistent way. This document introduces the iStar 2.0 core language, evolving the basic concepts of i* into a consistent and clear set of core concepts, upon which to build future work and to base goal-oriented teaching materials. This document was built from a set of discussions and input from various members of the i* community. It is our intention to revisit, update and expand the document after collecting examples and concrete experiences with iStar 2.0.