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The aim of this short survey is to give a quick introduction to the Salvetticomplex as a tool for the study of the cohomology of Artin groups. Inparticular we show how a spectral sequence induced by a filtration on thecomplex provides a very natural and useful method to study recursively thecohomology of Artin groups, simplifying many computations. In the last sectionsome examples of applications are presented.

Salvetti complex, spectral sequences and cohomology of Artin groups