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This is a translation in English of version 5 of the article arXiv:1404.3998,which is itself an introduction to arXiv:1209.5352. We explain all the ideas ofthe proof of the following theorem. For any reductive group G over a globalfunction field, we use the cohomology of G-shtukas with multiple modificationsand the geometric Satake equivalence to prove the global Langlandscorrespondence for G in the "automorphic to Galois" direction. Moreover weobtain a canonical decomposition of the spaces of cuspidal automorphic formsindexed by global Langlands parameters. The proof does not rely at all on theArthur-Selberg trace formula.

Introduction to chtoucas for reductive groups and to the global Langlands parameterization