You may read an introduction and outline of 2 Timothy here.
A prayer from Gregory of Nazianus [ (329-389) an early Church father] for your use before reading.
I. 1:1-2 Salutation
II. 1:3-4:8 Body of Letter
A. 1:3-2:13 Exhortations to Timothy
1. 1:3-5 Thanksgiving
2. 1:6-18 Do Not be Ashamed
3. 2:1-13 Share in Suffering: A repetition of the previous section, be strong, pass on the teaching of Paul, and share in suffering. Then three common examples, soldier, athlete, farmer. Finally Paul as example. Verse 11-13 is probably from an early Christian hymn.
B. 2:14-3:9 Warnings about Opponents: Exhortations and warnings.
1. 2:14-26 False Teaching and Senseless Controversy: Verse 17 gives a clue about the problems Timothy faces. Scholars think the opponents believed in a spiritual resurrection ( while the body was still on earth) and a body- spirit dualism which also included celibacy. We do not know anything more about the people named in verse 17 and 1 Tim 1:20. Notice in verse 24-25 how Timothy is to treat his opponents.
2. 3:1-9 Last Days: The language about the last days is not to predict the end, but to explain what is happening. Verse 6-7 uses cultural stereotypes about women (the efforts of women to learn philosophy were ridiculed by famous authors) to belittle the teachers by way of belittling their students. There is evidence in 1 Timothy 2:14 and 5:15 that some women were learning from opposing teachers. Jannes and Jambres were the names giving in extra-biblical texts to the Egyptian magicians who opposed Moses in Exodus 7:11,22.
C. 3:10-4:8 The Final Charge
1. 3:10-13 The Example of Paul’s Life: Paul as example
2. 3:14-4:5 The Formal Charge: Exhortations to faithfulness in 3:14-17. Remember “Scripture” in this context means the Hebrew Bible. Then 4:1 begins a formal charge to Timothy. The theme is the same as earlier in the letter.
3. 4:6-8 Completion of Paul’s Ministry: Allusions to Paul’s death. Jews wore crowns/wreaths of leaves or flowers as symbols of joy and honor at weddings and feasts. The Greeks gave wreaths/crowns to the winners of athletic competitions.
III. 4:9-22 Conclusion: now personal instructions, information, greetings and a benediction.
A. 4:9-15 Travel Arrangements: Recall 1:4 when Paul “longs” for reunion with Timothy. Notice the statements of abandonment and opposition which are consistent with concerns in other parts of the letter. Many of the names here are found in Acts or other letters.
B. 4:16-18 The First Defense: Desertion by humans, rescue by God.
C. 4:19-22 Final Greeting: Greetings were normally at the end of a letter.
Read More About It
Bassler, Jouette M. “1,2 Timothy and Titus” in HarperCollins Bible Commentary, rev. ed.James L Mays, ed. (New York: Society of Bible Literature) 2000.
Johnson, Luke Timothy, The Writings of the New Testament: An Interpretation, rev. ed. (Minneapolis:Fortress Press) 1999. Chapter 19 “The Pastoral Letters:1 Timothy, 2 Timothy, Titus.
Quanbeck, Warren,Beardslee, William A. “2 Timothy” in The New Oxford Annotated Bible, Bruce M. Metzger, Roland E. Murphy eds. (New York: Oxford University Press) 1994.