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The dimension of a vector space is an elementary and crucial concept in linear algebra. The lack of a basis in a module has lead to many alternative notions to measure the size and quality of rings and their modules. We will survey some of these alternative notions, like Global, Krull and Gelfand-Kirillov dimension, and will discuss when the usual dimension formula holds for the Goldie dimension of modules over a ring. The last part is based on a joint work with Edmund Puczylowski.