In 1 Peter he uses the name Peter, the Rock. Here in 2 Peter he addresses himself as Simon Peter. And he also describes himself as a servant of Jesus. 

2 Pet 1:2
Grace and peace be yours in abundance through the knowledge of God and of Jesus our Lord.
Grace and peace in abundance are promised to us through Jesus. Only through Him do we get real peace. But we get that grace and peace through the knowledge of God and of Jesus. Peace increases as we know Him better. We cannot just know about Him, we must know Him.

2 Pet 1:4
Through these he has given us his very great and precious promises, so that through them you may participate in the divine nature and escape the corruption in the world caused by evil desires.

Peter lists the qualities necessary to go beyond knowledge and into love and he says, 

2 Pet 1:8
For if you possess these qualities in increasing measure, they will keep you from being ineffective and unproductive in your knowledge of our Lord Jesus Christ.
We certainly do not want to be ineffective and unproductive on our knowledge of Him.

2 Pet 1:15
…and I will make every effort to see that after my departure you will always be able to remember these things.
Boy, did he ever!!! You are remembering them now…here…wherever you are at this moment.

2 Pet 1:18
We ourselves heard this voice that came from heaven when we were with him on the sacred mountain.
Peter is referring to the Mount of Transfiguration in which he, James, and John witnessed the appearing of Moses, Elijah, along with Jesus.

Peter, along with the other writers of the New Testament consistently warn of the dangers of false teaching. Peter uses the phrase, "exploit you with stories they have made up." We must be extremely careful of what we hear, see, or read. 

2 Pet 2:4
For if God did not spare angels when they sinned, but sent them to hell, putting them into gloomy dungeons to be held for judgment;

KJV uses “chains of darkness” in place of “gloomy dungeons”. Satan and his demons are like dogs on a chain. They are only allowed to move and do just so much, only what God allows them to do depending on the length of their “chain”.

2 Pet 3:1
Dear friends, this is now my second letter to you. I have written both of them as reminders to stimulate you to wholesome thinking.

If we read God’s Word we will be stimulated to wholesome thinking. If our minds are filled up with wholesome thinking, we won’t have room for unwholesome thinking. Peter tells us that this is his reason for writing both of the letters.

2 Pet 3:9a
The Lord is not slow in keeping his promise, as some understand slowness.Or to quote my dad (Patti’s)…”I know you’ll keep your promises, Lord, I just wish you wouldn’t wait until the last minute.”