These notes constitute the content of the series of lectures Introduction to local zeta functions by the second author, in the Lluís Santaló Research Summer School 2019:
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-Adic Analysis, Arithmetic and Singularities, June 24-28, at the Palacio de la Magdalena in Santander. We want to thank the organizers of the school for their excellent work.
The lectures were intended as an elementary introduction to
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-adic Igusa zeta functions and related topics. We hope that these notes reflect that goal. Our text is complementary to the one of León-Cardenal and Zúñiga-Galindo [Rev. Integr. Temas Mat., 37, 2019, 45–76]. The notes of Nicaise [MSJ Mem., 21, 2010, 141–166] are an introduction to
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-adic and motivic zeta functions. Substantial survey articles are the \lq old\rq Bourbaki report of Denef [Séminaire Bourbaki, 1990/91, 1992, 359–386] and the more recent paper of Meuser [Amer. J. Math., 138, 2016, 149–179].