This brief intro sets the scene for both letters as they have some things in common (as you might have guessed already!) For instance, the first two verses of both 1 and 2 Timothy clearly present the author as Paul and the recipient as Timothy. In this sense, along with the book of Titus, they are unique in the whole bible as personal letters written by a mentor to his mentee. Timothy is mentioned not only in Acts but also in many of Paul’s other letters. It is probable that he was converted to the Christian faith during Paul’s first missionary journey. He was closely associated with the apostle on the second and third journeys. In Phil. 2:19–20 Paul speaks warmly of Timothy’s care and concern. It is small wonder, therefore, that two personal letters are preserved addressed to Paul’s well-loved companion.
The most likely date for their composition is the mid-sixties (the exact years are disputed), when Paul was imprisoned in Rome. On this view, it is common to hold that Paul was released from the imprisonment mentioned at the end of Acts but was shortly rearrested and finally martyred, and that some of the events referred to in the letters to Timothy and Titus took place during this brief period of liberty. Certainly, 2 Timothy sounds as if it was written by someone who knew that his time was short.
The theme of 1 Timothy is that the gospel leads to practical, visible change in the lives of those who believe it. It is often thought that the theme is church order, but the discussion of church offices is simply a piece of the larger argument that the true gospel, in contrast to false teaching, will always lead to godliness in its adherents. First Timothy is a clear call for the church to live out in tangible ways the ethical implications of the gospel.
In 2 Timothy, Paul is writing a final exhortation to Timothy to urge him to stand firm and to ask him to come for one final visit before Paul is executed. Second Timothy is very personal, as would be expected in a final letter to a close friend and coworker. Paul exhorts Timothy to continue in faithfulness and points to his own life as an example for Timothy to follow. What he calls on Timothy to do, he himself has done already. Second Timothy is a bold, clear call for perseverance in the gospel in spite of suffering. Paul calls on his young coworker to continue the fight of faith, even as Paul approaches the end of his own life.
Mitch (exercising much plagiarism – see ESV study bible and New Bible Commentary).