In the Old Testament, the phrase the last days generally refers to a future time (see Jeremiah 49:39; Ezekiel 38:16; Hosea 3:5). In the New Testament, it refers to the period that started with the arrival of Jesus (Hebrews 1:2). More specifically, it refers to the time just before the end of the current age (2 Peter 3:3).
The mountain of the Lord’s house refers to the Temple Mount. This place symbolizes God’s glorious exaltation (see Isaiah 6:1) and his kingdom on earth. Isaiah’s focus on God’s supreme kingship comes from his famous vision of God (Isaiah 6).
Isaiah’s prophetic hope was not a narrow nationalistic dream. It included people from all over the world, beyond Judah and Jerusalem.