"For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God. But by the grace of God I am what I am, and his grace to me was not without effect. No, I worked harder than all of them - yet not I, but the grace of God that was with me." NIV translation
Paul continues by humbly explaining the fact that he didn't consider himself to be worthy of the title of an apostle or even salvation through Jesus Christ. But, because God selected and empowered him, he was able to serve the Lord and become the greatest evangelist the world has ever seen.
"Whether, then, it is I or they, this is what we preach, and this is what you believed." NIV translation
Paul reminds them that there is only one gospel and that the same message was shared by all of the apostles. In our world today, it seems like many pastors and teachers are looking for a clever message. As we see here, the simple gospel that was preached by the apostles is what is needed.
"But if it is preached that Christ has been raised from the dead, how can some of you say that there is no resurrection of the dead?" NIV translation
Paul asks a simple question in hopes of getting the people to see the fact that you cannot take a part of the gospel and the philosophy of the day and combine them. The same type of thing is happening in our world today as many want to accept the fact that Jesus was a prophet but they deny that He was and is the Son of God.
"If there is no resurrection of the dead, then not even Christ has been raised. And if Christ has not been raised, our preaching is useless and so is your faith." NIV translation
Paul goes on to explain that you cannot have it both ways. Either the resurrection of man from the dead happens as in the case of Jesus or it does not happen at all. If you do not believe in the resurrection, then, nothing else matters. If Jesus had lied about His resurrection, then, you could not believe anything He had said.
"More than that, we are then found to be false witnesses about God, for we have testified about God that he raised Christ from the dead. But he did not raise him if in fact the dead are not raised." NIV translation
The penalty for being a false witness about God, was death and so Paul makes it clear how much he believes in the resurrection.