Authorship and Audience
In terms of authorship, this book is among the most widely disputed books in the New Testament. When mentioning the book, Origen (185 - 253) notes that there were some who disputed Petrine authorship of this book. Many modern scholars concur in saying that Peter was not the author of 2 Peter. There is a good discussion of this debate in the "Introduction" section here. I will leave it to you to investigate these claims as there has already been much ink spilled about the subject and I have nothing more to contribute. Personally, I accept Petrine authorship for the reason discussed in the paragraph below.
I want to make one note regarding authorship. Probably the most compelling (and certainly the most common) argument against Petrine authorship is the significant difference in the quality and character of the Greek used in 1 Peter versus that of 2 Peter. The logic goes something like: "If the Greek used in 1 Peter and 2 Peter are so different, Peter can't have written them both". My response would be that 1 Peter 5:12 which implies that Silvanus was an amenuensis who wrote what Peter dictated. As such, Peter, who may have been more eloquent in speech than in writing, could simply speak the things he wanted to say. Thus, it is possible that Peter authored 1 Peter by dictating to Silvanus and wrote 2 Peter with his own hand.
As to the audience of this book. verse one states that the audience is believers. 2 Peter 3:1 likely refers to 1 Peter, so it is reasonable to assume that the audience of 2 Peter had received or was familiar with 1 Peter (see Authorship and Audience section for that book). 2 Peter 3:15 also notes that the audience had received a letter from Paul at one point. Although we don't know of any Pauline letter addressed to believers in the churches mentioned as the audience of 1 Peter, it could be that Paul's letters were passed around to those churches or that Paul had written other letters of which we are not aware.
Date and Context
The Roman Emperor Nero died in 68 AD. If tradition is correct in claiming that Peter was martyred by Nero, the letter must have been written before or during 68 AD. 2 Peter 1:14 shows that Peter thought his death was imminent which dates the letter shortly before or during 68 AD at the latest.
2 Peter has a lot of connections with other letters in the New Testament. 2 Peter is the second letter that Peter wrote (2 Peter 3:1), some of its themes and content echo Jude, and it references Paul's letters (3:15-16). Like many of the letters written later in an Apostle's life, it has a distinctly 'final' feel to it in that it feels like reading the last instructions from a father to his children (e.g. 2 Peter 1:12-15).
0. Introduction [1:1-11]
A. Greeting [1:1]
B. Admonition to Grow [1:2-11]
I. Thesis: Remembering the Important Things [1:12-15]
II. Characteristics of True Revelation [1:16-21]
III. Characteristics of False Teaching and Teachers 
IV. Reiteration of Thesis [3:1-2]
V. Christ's Return [3:3-13]
VI. Closing Admonitions [3:14-18]
I believe that 2 Peter 3:1-2 and 3:17-18 sufficiently summarize the themes of this book.
3:1-2: "This is now, beloved, the second letter I am writing to you in which I am stirring up your sincere mind by way of reminder, that you should remember the words spoken beforehand by the holy prophets and commandment of the Lord and Savior spoken by your apostles."
3:17-18a: "You therefore, beloved, knowing this beforehand, be on your guard so that you are not carried away by the error of unprincipled men and fall from your own steadfastness, but grow in the grace and knowledge of our Lord and Savior Jesus Christ."
- Guard against false teaching. Following Christ requires that we are constantly guarding ourselves against falsehood and the lies that would draw us away from Christ. In this letter, Peter spends time detailing specific details about false teaching so that his readers can be equipped to detect and avoid false teaching. It is no small matter to Peter and it should not be to us either.
- Grow in Christ. If we are to avoid false teaching about Christ, we are also supposed to pursue and grow in the truth about Christ (see 2 Peter 3:18 and 1:5-8).
- The importance of divine revelation. As Peter addresses false teaching and the necessity of growing in knowledge of Christ, he presents divine revelation, whether Old Testament scripture or eye-witness accounts from the Apostles, as the necessary foundation for both of these actions (2 Peter 1:16-21 and 3:1-2). According to Peter, correctly interpreting scripture is a critical step in growing in Christ and avoiding false teaching (see Peter's mention of Paul in 3:15-17).
- The importance of remembering. I would be remiss if I did not mention that "remembering" is a critical theme of this book. One of Peter's major gaols for this book was the remind his readers of the truths they already knew ( see 2 Peter 1:12-15 and 3:1-2).
- Unlike 1 Peter, there are very few, Old Testament quotations in 2 Peter.