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FERREIRA, G. R. Symmetries of Julia sets for analytic endomorphisms of the Riemann sphere. 2019. 47 pages. Dissertation (MSc.) – Institute of Mathematics and Statistics, University of São Paulo, São Paulo, 2019. Since the 1980s, much progress has been done in completely determining which functions share a Julia set. The polynomial case was completely solved in 1995, and it was shown that the symmetries of the Julia set play a central role in answering this question. The rational case remains open, but it was already shown to be much more complex than the polynomial one. In this thesis, we review existing results on rational maps sharing a Julia set, and offer results of our own on the symmetry group of such maps.