Intro to 2 Timothy 2

Here are the opening words from 2 timothy 1:

1Paul, an apostle of Christ Jesus by the will of God according to the promise of the life that is in Christ Jesus,

2To Timothy, my beloved child:

Grace, mercy, and peace from God the Father and Christ Jesus our Lord.

This is a book written by Paul.

Paul is an apostle of Christ Jesus by God's will. This is according to the promise of life that is in Christ Jesus.

It is written to Timothy, who Paul calls his beloved child.

Paul extends a greeting "grace, mercy and peace from God the Father and Christ Jesus our Lord".

Looking at this a bit more...
Paul was chosen by God to be an apostle. It wasn't Paul's decision, it was God's good pleasure that made Paul an apostle. It was God's good pleasure, God's choice that gave Paul life in Christ Jesus.

One of the e-sword commentators mentioned that the word used for "beloved child" implied a measure of respect. Timothy had showed himself to be a man of God, and since he was younger in years, Paul claimed him as a spiritual son. This is how JFB put it :

But this {thinking of it as mere love or affection} seems to me not justified by the Greek word agapetos, which implies the attachment of reasoning and choice, on the ground of merit in the one “beloved,” not of merely instinctive love.

And then what I think of as a standard greeting is issued to Timothy. Grace, mercy and peace. All three. Shows that grace and mercy are different. He is asking for God's favour to be on Timothy, for God's mercy to be shown him, and for him to be free from the affects of war on his life. This all from God the Father and Christ Jesus the Son.