Black holes play an increasingly important role in the study of gravitational physics. In this mini lecture series, aimed at graduate students with no prior experience in general relativity, we will first review the basics of curved spacetime, including a bit of mathematics but also drawing on physical intuition. In a second step, we will focus on black holes, explain some of their properties, and highlight what fundamental physics questions can be answered with current and planned observations of black holes. Last, in a third step, we will take a peek into the future, and address current theories (such as black hole thermodynamics, holography, and non-singular gravity) that address quantum aspects of black holes and connect the rich field of gravity to quantum physics itself.