Geometry has come a long way from the times of triangles and conic sections. I will try to explain what kinds of objects geometers and topologists work with these days. We will then look at the moduli problem, which is concerned with classifying and parametrising families of geometric objects. The main idea is to turn a collection of geometric objects itself into a geometric object. This is an extremely fruitful approach, but it is also very delicate and will quickly force us to rethink what we mean by a geometric object,

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