Antonio Díaz Ramos Departamento de Ãlgebra, Geometría y Topología Facultad de Ciencias Universidad de Málaga Spain Title: A spectral sequence for fusion systems. Abstract: We build a spectral sequence converging to the cohomology of a fusion system. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence but does not always coincide with it. We give examples and prove Tate's $p$-nilpotency criterion following its original proof and using this new spectral sequence.