This one came in chunks.  Some of it is difficult as it delves into the deep theology of the sovereignty of God in relation to free will and sin.  Finding the context from which Paul wrote is paramount or his words don’t make sense.  Full text understanding is necessary.

Romans 9:6-13   Paul illustrates that God’s purpose in Israel as the Chosen People deals more with the spiritual aspect than the physical.  It is not enough to just be a physical descendant of Abraham, but one of his faith which was counted as righteousness.

7  “Neither, because they are the seed of Abraham, are they all children…”
8  “…these are not the children of God: but the children of the promise are counted for the seed”
Abraham had many sons, but only Isaac was the son of promise.  Only his descendants were the people of God.  Likewise, just being a physical descendant isn’t enough.  You must be a spiritual one.  This opened the entire world to the redemption of God as He planned.  If anyone, Jew or Gentile, believe in Christ in faith as Abraham did, it will be counted to them as righteousness.  This will be touched on later in the chapter.

14-24   The hard section.
18  “Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth”
Paul then asks the obvious question, why does God find fault, if He is the one making the determination.  Verses 20 and 21 point out that God is God and we are not.  Commentary also mentioned that Paul’s context points to us not as just God’s creation, but as a sinful creation.  We, none of us, deserve any of God’s mercy.  Therefore, He is totally justified to do as He pleases.  It is good here to remember the whole context of scripture to stay on track.
II Peter 3:9  “[The Lord is] not willing that any should perish, but that all should come to repentance.”

22  “…endured with much longsuffering the vessels of wrath fitted to destruction”
I think this is the point of the section.  God in His mercy is still longsuffering even with those who will not come to Him.  Reminds me of the time He gave the Canaanites before He sent Israel into the Promised Land.

25  “…I will call them my people, which were not my people…”
As mentioned earlier, the Gentiles would be included as part of the promise if they show the faith of Abraham.

29  “…Except the Lord of Sabaoth had left us a seed, we had been as Sodoma, and been made like unto Gomorrha”
God made His promise to Abraham through Isaac.  He will fulfill that promise by always having a remnant of the House of Israel.  He did not replace Israel with the family of God, those who believe in Christ, and this points to that.  The remnant is still here so the original promise is intact.  Replacement Theology has no grounds.  The family of God has been grafted into the promise.

30  “…Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith”
Gentiles did not have the law, but can attain righteousness through faith.

I hope you enjoy reading and studying His word.  May it accomplish what He desires.  Please feel free to comment or post questions.  Thanks for reading!