In this episode of well-defined & wonderful, we introduce the concept of a metric space. In order to rationalise the definition of this abstract concept, we go through elementary examples from ``practice’’ to build up our intuition. The core concept we want to mathematically describe and understand is the notion of distance. A metric space is then a mathematical object where distances of the elements in this space can be measured using a metric. In order to be justifiable as a mathematical model of distances in practice we single out a couple of properties we want the metric to satisfy. These properties and why detours are really detours and no shortcuts are also explained in this episode. Gladly Fabian Gabel helped again to gather these ides in a structured manner.