Albert Barnes Commentary Daniel 8:21

"And the rough he-goat is the king of Greece: and the great horn that is between his eyes is the first king." — Daniel 8:21 (ASV)

And the rough goat - See the notes on Daniel 8:5. In Daniel 8:5 he is called a he-goat. Here the word rough or hairy – שׂעיר s'â‛ı̂yr – is applied to it. This name is often given to a goat (Leviticus 4:24; Leviticus 16:9; Genesis 37:31). It would seem that either term – a he-goat, or a hairy-goat – would serve to designate the animal, and it is probable that the terms were used indiscriminately.

Is the king of Grecia - Represents the king of Greece. The word here rendered Grecia (יון yâvân) usually and properly denotes Ionia, the western part of Asia Minor; but this name was extended to embrace the whole of Greece. See Aristophanes, Acharnians, 504, and the scholia on that passage; Aeschylus, Persians, 176, 561; Gesenius' Lexicon, the Latin Vulgate, and Theodotion here render it “the king of the Grecians,” and there can be no doubt that the royal power among the Greeks is referred to here. See the notes on Daniel 8:5.

And the great horn that is between his eyes is the first king - Alexander the Great. The first that consolidated the whole power, and that was known in the East as the king of Greece. So he is expressly called in 1 Maccabees 1:1: The first over Greece. Philip, his father, was opposed in his attempts to conquer Greece, and was defeated. Alexander invaded Greece, burned Thebes, compelled the Athenians to submit, and was declared generalissimo of the Grecian forces against the Persians.