  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 of
the proof of the following theorem. For any reductive group G over a global
function field, we use the cohomology of G-shtukas with multiple modifications
and the geometric Satake equivalence to prove the global Langlands
correspondence for G in the "automorphic to Galois" direction. Moreover we
obtain a canonical decomposition of the spaces of cuspidal automorphic forms
indexed by global Langlands parameters. The proof does not rely at all on the
Arthur-Selberg trace formula.
