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The TeXbook doesn't explain ligatures more than presenting the existing ones, the same for TeX By Topic. So, how are they defined? Is there a third way besides active characters and control sequences to ask TeX to do something unusual? Can we create new ones?

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Ligatures are defined in either the .tfm or .vf: http://tug.org/tugboat/tb11-1/tb27knut.pdf

or in the font itself if using a non-TeX (.tfm or .vf) font using a TeX-variant such as XeTeX or LuaTeX.

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