This book provides an introduction to projective geometry, with algebraic details kept to a necessary minimum for the proofs. To be able to illustrate the concepts, we focus on the real projective plane. The central theme is conic sections and their relationships - here, the clarity achievable through the projective approach is particularly evident. We will engage in geometry without measuring. We also want to understand how the Euclidean plane - our usual geometric conceptual world - is a singular limiting case and how this can help us understand geometric concepts. Many of the discussed topics can be visualized and explored using an interactive application on the author's website.