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Enter a fascinating world where the normal rules of geometry change and open the way to incredible discoveries. Do you remember anything from elementary school geometry? Whether yes or no, you might be interested in how its content can be turned on its head. In history, one simple question was enough for the gradual discovery of new exotic worlds in which the known rules are easily twisted. Together we will look under the hood of two non-Euclidean geometries - hyperbolic and elliptic. We discover that parallels can intersect or that not every triangle has an interior angle sum of 180°. We will talk about what a straight and curved surface means and what a straight line is. We'll discover how these and other seemingly abstract concepts affect the real world, what role these unusual geometries play in the world of physics, and how they're crucial to explaining general relativity and the mysteries of the universe.