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 Peter 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 Peter 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 Peter 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 in our knowledge of Him, therefore we must possess those qualities in increasing measure.  Maybe we should go back and reread those qualities!

2 Peter 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, as you are reading this.

2 Peter 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.  They heard the voice of God telling them to listen to His Son. 

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. It must be consistent with Scripture and especially the teachings of Jesus.

In 2 Peter 1:16-21 Peter reminds us that the Old Testament prophecies were for the coming of the Messiah.  The New Testament prophecies are for the triumphant return of the Messiah.  Prophecies were (and are) as lights of hope until the day dawns and Jesus comes (or returns).

In the second chapter of 2 Peter, he warns of the danger of false teachers.  There are numerous parallels to the book of Jude.

2 Peter 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 allowed to move and do only what God allows them to do depending on the length of their “chain”.  The word hell is the Greek word tartaroo.  The definition of this word is the Abyss, the home of the wicked where they await their future punishment.  This verse in 2 Peter is the only reference to tartaroo in the New Testament, and this is in reference to fallen angels, beings that cannot die and will suffer torment for eternity.

More details concerning this can be found in the book These Last Days Second Edition by Phil and Patti Moore. 

2 Peter 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 Peter 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.”