TITLE: Reference request: the geometry of vanishing cycle
QUESTION [6 upvotes]: I’m currently studying basics on étale cohomology, by Fu’s and Milne’s book. The formalization of vanishing cycle and nearby cycle particularly interests me. I realized it may relate with reduction and model problems (for example, Oda’s  A Note on Ramification of the Galois Representation on the Fundamental Group of an Algebraic Curve.)(However, I’m also a beginner on these problems.) I want to learn more about nearby cycles and vanishing cycles, but the classical reference SGA7 is not available as reading French is quite difficult for me (especially reading something new). I have learned the elementary definition and motivation. So are there any textbook, online notes or videos on this topic, with enough detail?

REPLY [4 votes]: Luc Illusie has written two great expository texts on étale vanishing cycles and other topics in SGA7, one in English (with an associated set of slides) and one in French (unfortunately).
Illusie has also written two interesting articles about more advanced topics on étale vanishing cycles, which may still be valuable to you if you want to understand some recent developments: one on the Thom-Sebastiani theorem and one on vanishing cycles over higher-dimensional bases