Men and brethren
Dispensationally, this is the most important passage in the N.T. It gives the divine purpose for this age, and for the beginning of the next.
(1) The taking out from among the Gentiles of a people for His name, the distinctive work of the present, or church-age. The church is the ecclesia--the "called-out assembly." Precisely this has been in progress since Pentecost. The Gospel has never anywhere converted all, but everywhere has called out some.
(2) "After this viz. the out-calling I will return." James quotes from Amos 9:11; Amos 9:12. The verses which follow in Amos describe the final regathering of Israel, which the other prophets invariably connect with the fulfilment of the Davidic Covenant (e.g.); Isaiah 11:1; Isaiah 11:10-12; Jeremiah 23:5-8.
(3) "And will build again the tabernacle of David," i.e. re-establish the Davidic rule over Israel 2 Samuel 7:8-17; Luke 1:31-33.
(4) "That the residue of men Israelites may seek after the Lord" cf Zechariah 12:7; Zechariah 12:8; Zechariah 13:1; Zechariah 13:2.
(5) "And all the Gentiles," etc. cf Micah 4:2; Zechariah 8:21; Zechariah 8:22. This is also the order of Romans 11:24-27.