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I am an Indian citizen with a US green card. I am going on a study abroad trip to London and I know I need a visa for that. However, I do plan to take a trip to Germany to visit my relatives via train (EuroStar and the ICE). I know the trains have stopovers in either Paris or Brussels but I am unsure of what the visa requirements will be for these countries, especially for France and Belgium since I would just be switching trains. I assume I would need a German visa as well.
What kind of permission do I need for traveling through these countries?