In mathematics, an algebraic stack in algebraic geometry is a special case of the concept of a stack, which is useful for working on moduli questions.

There are two main classes of stacks, Deligne-Mumford stacks (DM stacks) and Artin stacks . The initial construction requires a category fibered in groupoids (CFG), and adds two conditions

1. a requirement for extending diagrams via cartesian squares, and
2. the ability to "glue" morphisms and objects, similar to the gluing of local affine spaces into schemes.

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For a good introduction to algebraic stacks, see the website of William Fulton.