تَبَارَكَ ٱلَّذِى نَزَّلَ ٱلْفُرْقَانَ عَلَىٰ عَبْدِهِۦ لِيَكُونَ لِلْعَٰلَمِينَ نَذِيرًا
"Blessed is He who sent down the Furqān upon His servant, that he might be a warner to all the worlds!"
Root ب-ر-ك: the core sense the lexicographers give is baraka — the kneeling of a camel, settling in a place and staying fixed there. From this comes the sense of baraka (a good that lasts and increases). The root was treated at al-Mulk 67/1 (tabāraka'lladhī bi-yadihi'l-mulk). I do not repeat it here.
The word occurs three times in this sūra: 1, 10, 61. This is a pattern that can be verified from the text, and the subjects of the three occurrences differ: the book, the promise, the sky.
The root ف-ر-ق: to separate, to open a gap between two things. The root was treated at al-Dukhān 44/4 (yufraqu kullu amrin ḥakīm) and in al-Mursalāt.
Furqān — the pattern (fuʿlān) is counted by the lexicographers as a noun of action: "the act of separating", or "that which makes distinct".
I record this as an observation: this name given to the book states not its content but its function. And the whole of the sūra is that function put into practice: through the verses two parties, two sayings, two walks, two waters, two ends will be separated.
عَلَىٰ عَبْدِهِ — "upon His servant". The designation is worth recording: the objection that will come in the seventh verse will be aimed at exactly this point — mā li-hādha'r-rasūli yaʾkulu'ṭ-ṭaʿām. At the very outset the verse says that the one sent is a servant.
ٱلَّذِى لَهُۥ مُلْكُ ٱلسَّمَٰوَٰتِ وَٱلْأَرْضِ … وَخَلَقَ كُلَّ شَىْءٍ فَقَدَّرَهُۥ تَقْدِيرًا — taqdīr: the root ق-د-ر was treated at al-Qadr, al-Qamar 54/49 and al-Zumar 39/67 — the core sense is measure. I do not repeat it here.