Despite spectacular recent progress, there is still a lot we don't know about our universe. We don't know why the Big Bang happened. We don't know what most of the universe is made of. We don't know whether there is life in space. We don't know how planets form, how black holes get so big, or where the first stars have gone. This course will take you through nine of the greatest unsolved problems of modern astrophysics. We can't promise you the answers, but we will explain what we do and don't know, and give you an up-to-date understanding of current research. This course is designed for people who would like to get a deeper understanding of these mysteries than that offered by popular science articles and shows. You will need reasonable high-school level Maths and Physics to get the most out of this course. This is the first of four ANUx courses which together make up the Australian National University's first year astrophysics program. It will be followed by courses on exoplanets, on the violent universe, and on cosmology.