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== Introduction ==
regularity method is a powerful tool that refers to the combined application of hypergraph regularity lemma and associated counting lemma. It is a generalization of graph regularity method, which refers to the use of Szemerédi's regularity and counting lemmas.
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This is an extension of Szemerédi's regularity lemma that decomposes any given graph into pseudorandom blocks, namely <math> \varepsilon </math>-regular pairs, and graph counting lemma that estimates number of copies of a fixed graph as a subgraph of a larger graph.
There are several distinct formulations of the method, all of which imply hypergraph removal lemma and a number of other powerful results, such as Szemerédi's theorem, as well as some of its multidimensional extensions.
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== Definitions ==
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