This is probably very simple but I couldn't find anything about in the usual latex guides. In this phrase:
{\em hello\/}
what is the purpose of the "\/" ?
This is a so-called italic correction. Its purpose is to ensure proper spacing after italic text.
Example:
{\itshape M}M produces MM, but italics M touches normal M.{\itshape M\/}M produces M M, with a bit more spacing to avoid touching.\/ is also the standard macro for separating letters which would otherwise form a ligature, so as said before it acts as a separator. But if you’re using the packages german/ngerman (deprecated), or babel with option german/ngerman (I don’t know at the moment whether it works on other languages as well) you can take "| which generates slightly better spacing and does not influence the hyphenation, as \/ would.
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