Proto-Indo-European *dʰwer- "door, doorway" is the source of English door.
In Latin, *dʰwer- became forīs and forās "out of doors", whence Old French forest. We also get forum and foreign from the Latin forms.
In Greek it became θύρα "door", and θυρεός "shield", then thyroid, because the thyroid is shaped like a shield.
In Indo-European Languages and Culture, Fortson says we have reconstructed a word for "door jamb" but doesn't say what it is. It must be this one, also here, which I'll write as *h₂énh₁t(e)h₂. It's found in anta from Latin antae "pilasters".