This course covers the axiomatic approach to geometry, similar and congruent triangles, quadrilaterals, polygons, circles, power of a point, three-dimensional geometry, transformations, introductory trigonometry, analytic geometry, geometry on a sphere, hyperbolic geometry, and more. The class blends the Art of Problem Solving (AOPS) and the Russian math approaches. We follow the curriculum outlined in the AOPS textbooks supplementing it with a well-defined course structure, rigorous proofs, and continuous review. A particular emphasis is placed on logic, connections between new and previously learned concepts, and a systematic approach to challenging problems. The first hour of each lesson is devoted to learning new concepts and proving key theorems. The last 30 minutes of the class are typically spent on solving challenging problems and/or additional practice. ​