Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In algebraic geometry, an algebraic stack is a concept introduced to generalize algebraic varieties, schemes, and algebraic spaces. They were originally proposed in a 1969 paper by Pierre Deligne and David Mumford to define the (fine) moduli space of genus g curves; their definition is currently referred to as Deligne–Mumford stacks. When viewed in this light, algebraic stacks are an algebraic analogue of orbifolds. They were generalized by Michael Artin in 1974 to what is now called an Artin stack, or sometimes, confusingly, an algebraic stack.

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