Chapter 54 part 2 & 3 Class handout - The Barren Becomes Fertile.
In 51 & 52 The LORD revealed Himself as the LORD the Jews wanted, but refused to believe in Him. In Chapter 53 The LORD reveals The Messiah they needed, not the messiah they looked for or wanted.
We know as a nation the Jews rejected the Messiah they sent to the cross. (De 21:23, Galatians 3:13)
The nation of Israel once again contented with their Maker on His choice of a shepherd. 45:9&10 all over again. The LORD knew this was going to happen.

Isaiah 54:1 ¶ Sing, O barren, thou that didst not bear; break forth into singing, and cry aloud, thou that didst not travail with child: for more are the children of the desolate than the children of the married wife, saith the LORD.
Sarah is the mother of the nation of Israel, Hagar is the mother of nations that oppressed Israel.
Remember Chapter 50 lesson- The LORD tells Judah that He has not put them away as He had the northern kingdom (Jeremiah 3:8) The Law of Divorcement
Only about 43,000 returned to Jerusalem to rebuild the temple as Cyrus decreed. (From Judah)
The a few chose to be identified as children of the barren who was not put away by The LORD, the many chose to remain as children of the one put away by The LORD - spiritual desolation.
*The barren is the nation of Israel, Judah in particular and specifically, Jerusalem (verses 54:11-12) - These verses speak of That Day when the Jerusalem that now is with the new Jerusalem from above. So 54:1 is speaking of the Jerusalem that was at the time after
1) They rejected the decree of Cyrus (40-45)
2) They refused to believe The LORD of Isaiah was the LORD they wanted (51:9-11)
3) They refuse the LORD they needed (53)
Barren - This is the spiritual condition of Jerusalem in the past and present - Barren will break forth in singing in the Jerusalem of That Day. - In That Day there will still be only a remnant.

Isaiah 51:2 Look unto Abraham your father, and unto Sarah that bare you: for I called him alone, and blessed him, and increased him.
Abraham & Sarah were the examples of someone with believing faith that was accounted unto righteousness.
Heb 11:10 For he looked for a city which hath foundations, whose builder and maker is God.
Heb 11:11 Through faith also Sara herself received strength to conceive seed, and was delivered of a child when she was past age, because she judged him faithful who had promised.
Galatians 4 uses the story of Abraham, Sarah and Hagar to teach the difference between being born after the flesh and being born of the promise or Spirit. Isaac was the son of promise, Ishmael was the son of Hagar, an Egyptian bond woman, was the son of the flesh. Paul was dealing with Christians in Galatia who were being seduced into leaving the freedom of salvation by grace and placing themselves back under the bondage of the law. The LORD here addressing those Jews who chose to remain in captivity instead of returning to Jerusalem. The many
Isaiah 30:1 ¶ Woe to the rebellious children, saith the LORD, that take counsel, but not of me; and that cover with a covering, but not of my spirit, that they may add sin to sin:
Isaiah 31:1 ¶ Woe to them that go down to Egypt for help; and stay on horses, and trust in chariots, because they are many; and in horsemen, because they are very strong; but they look not unto the Holy One of Israel, neither seek the LORD!
The LORD is stating that there were many more who chose to give up the covering of His Spirit and live after the flesh. Only about 43,000 from the kingdom of Judah chose to follow The LORD's shepherd, Cyrus down the strait path to Jerusalem and proper worship. The rest chose to remain in the spiritual desolation, the flesh. Was it by chance that Hagar was Egyptian (Ishmael was half Egyptian) or was it by divine intervention? This is a picture of those vast majority Jews who would reject Christ at His first coming and chose to remain under the bondage of the law. [The barren woman should sing she bore no children of desolation. { is best to be a mother of no children or the mother of many whose end is desolation}]
Luke 21:23 But woe unto them that are with child, and to them that give suck, in those days! for there shall be great distress in the land, and wrath upon this people
*This verse is a summation of the nation of Israel, Judah in particular and specifically the city of Jerusalem.
Isaiah was given the opportunity to address their condition of their past, his present, our present and their future.
In Luke 21:23 the future of the Jews is the great desolation of those days of the Tribulation which leads to That Day (Isaiah  10:20 ¶ And it shall come to pass in that day, that the remnant of Israel, and such as are escaped of the house of Jacob, shall no more again stay upon him that smote them; but shall stay upon the LORD, the Holy One of Israel, in truth.) Why - [Isaiah 2:11; 4:2; 10:20; 10:27; 11:10; 12:4; 17:7] 

The main reason the heart of the nation - God’s Holy city of Jerusalem will be cleaned up, protected and glorified. Verses 11-17.
Verses 11-17 show that verse 54:1 is being addresses to His Holy City of "That Day" of Luke 21:23 leading to That Day of Zechariah 14:16. Jerusalem during the 1000 Kingdom of Christ ending with the last stand of Satan and all who choose to follow him against God's holy city. Revelation 20.
{1Chronicles 29:2; - Jerusalem that was and will be again during the 1000 yr kingdom of Christ and for eternity Revelation 21:18-19}

Verses 2-3 The seed of Abraham will explode in number and they will inherit the Gentiles (Genesis 22:15-19)
Isaiah 60:16 Thou shalt also suck the milk of the Gentiles, and shalt suck the breast of kings: and thou shalt know that I the LORD am thy Saviour and thy Redeemer, the mighty One of Jacob.
Isaiah  61:6 But ye shall be named the Priests of the LORD: men shall call you the Ministers of our God: ye shall eat the riches of the Gentiles, and in their glory shall ye boast yourselves.
Jeremiah 3:14-19 note verse 16 - In Those Days - The reuniting of the kingdom of Judah and Israel into one nation.

Verses 4 & 5 The promise that the past shame of God’s City being put away by The LORD their Maker.
Put away from their memory. Fear not the husband that did not put you away is The LORD - He is not through with His people or His city.