In the book of Acts, we find that a time came when Paul turned to the Gentiles with the gospel after following the command to take first the gospel to Israel:

(Act 13:44 KJV) And the next sabbath day came almost the whole city together to hear the word of God.
45 But when the Jews saw the multitudes, they were filled with envy, and spake against those things which were spoken by Paul, contradicting and blaspheming.
46 Then Paul and Barnabas waxed bold, and said, It was necessary that the word of God should first have been spoken to you: but seeing ye put it from you, and judge yourselves unworthy of everlasting life, lo, we turn to the Gentiles.

Paul was persecuted by the unbelieving Jews, but he remained steadfast in proclaiming the gospel. He told the unbelieving part of the nation that he had delivered to them the way of salvation, but they rejected it and thus judged themselves unworthy of everlasting life.

Paul didn't judge them. Paul says it is they who judged themselves as unworthy of eternal life because they rejected the gospel of Christ. But, that didn't stop Paul from travailing over them and loving them. In the opening verses of chapter 9 of Romans, Paul bares his heart concerning his "kinsmen according to the flesh," meaning the unbelieving Israelites:

(Romans 9:1 KJV) I say the truth in Christ, I lie not, my conscience also bearing me witness in the Holy Ghost,
2 That I have great heaviness and continual sorrow in my heart.
3 For I could wish that myself were accursed from Christ for my brethren, my kinsmen according to the flesh:
4 Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;
5 Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen.

Paul knows his being cut off from Christ would not save them, yet, with his knowledge of Christ, he knows there is nothing he can do for them because they must individually believe on Christ to be saved. He states that the Israelites had heard everything they needed to hear in order to be saved - the adoption, the covenants, the promises - and not only that, they were the ones through whom Christ came into the world, yet not all believed and these who would not believe were cut off from the Christ. Paul goes on to say, that, lest anyone should blame the word of God for failing, God's word didn't fail. They just didn't believe and in rejecting the good news pronounced their own judgment. He had called them kinsmen after the flesh, and he travailed over them, yet he now brings in another group, the seed of Abraham as the children of promise:

(Romans 9:6 KJV) Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
7 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.
8 That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.
9 For this is the word of promise, At this time will I come, and Sarah shall have a son.
10 And not only this; but when Rebecca also had conceived by one, even by our father Isaac;
11 (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth;)
12 It was said unto her, The elder shall serve the younger.
13 As it is written, Jacob have I loved, but Esau have I hated.

Paul distinguishes between Israel after the flesh and Israel after the promise. Israel after the flesh were those who sought righteousness under the law, while the children of promise were those who acquired a righteousness that came through faith in Christ. He refers to both groups as one, but only in reference to being born after the flesh, calling them all children of Abraham (or natural Israelites): "For they are not all Israel, which are of Israel." "Which are of Israel" refers to all the Jews, both the Jewsish believer and the Jewish unbeliever, but then Paul paints a picture of the believing Jews within natural Israel who are also called Israel, those born after the promise given to Abraham. This second group are those whom God chose to enter into a special relationship in order to bring His plan of salvation to the world. Paul said this election is by God's mercy and a sovereign act in His plan:

(Romans 9:14 KJV) What shall we say then? Is there unrighteousness with God? God forbid.
15 For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
16 So then it is not of him that willeth, nor of him that runneth, but of God that showeth mercy.
17 For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might show my power in thee, and that my name might be declared throughout all the earth.
18 Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.
19 Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
20 Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
21 Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
22 What if God, willing to show his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,

God's salvation is to show His mercy, not only to the Jew, but to the Gentile as well. For millennia, the Gentiles were not God's people, while He clearly states that the Israelites were His people. But now, since the furtherance of God's plan of salvation in Christ was rejected, Paul says even the Gentiles can come to a place where God says they, too, are His people:

(Romans 9:24 KJV) Even us, whom he hath called, not of the Jews only, but also of the Gentiles?
25 As he saith also in Osee, I will call them my people, which were not my people; and her beloved, which was not beloved.
26 And it shall come to pass, that in the place where it was said unto them, Ye are not my people; there shall they be called the children of the living God.

Paul, of course, is speaking of those Gentiles who would come to believe on Christ, but then he goes on to add them to the remnant of natural Israel:

(Romans 9:27 KJV) Esaias also crieth concerning Israel, Though the number of the children of Israel be as the sand of the sea, a remnant shall be saved:
28 For he will finish the work, and cut it short in righteousness: because a short work will the Lord make upon the earth.
29 And as Esaias said before, Except the Lord of Sabaoth had left us a seed, we had been as Sodoma, and been made like unto Gomorrha.
30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.

In Paul's time, some Jews and some Gentiles did not believe and therefore "stumbled at that stumblingstone." But, the remnant of Israel who came to righteousness through faith in Christ and the Gentiles who came the same way were one body in Christ. In the verses from Romans 9, Paul, therefore, set up four groups:

1. Jews who would not believe on Christ (Paul's kinsmen after the flesh)
   
2. Gentiles who would not believe on Christ
   
3. Jews who would believe on Christ (Paul's kinsmen after the promise)
   
4. Gentiles who would believe on Christ

The Jews and Gentiles who would not believe on Christ are the unbelievers. The Jews and Gentiles who would believe on Christ are the believers. So, all that Paul said can be summed up in these two groups.

This must have been a very heartbreaking chapter for Paul to write. You can almost feel his anxiety over Israel and the pleadings of his heart, and this sorrow and travailing went on in the next two chapters as well.

Some Simple Thoughts On Romans 9
Some Simple Thoughts On Romans 10
Some Simple Thoughts On Romans 11

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