As is common in his letters Paul starts off reminding the reader of his authorization, his appointed office as an apostle, which gives particular weight to his words and for this reason we study them.
Here we notice that of the many aspects of God and Jesus Christ, in this case he speaks of God our Savior and Jesus Christ our hope. Interesting that among other places he speaks of salvation in this letter, he speaks of God "desiring all men to be saved" (1Tim 2:4), and of "God, who is the Savior of all men, especially of those who believe." (1Tim 4:10) The hope is of course the feeling of anticipation of the salvation which is yet to be revealed.
So as we study through this letter we should keep in mind that whatever particulars Paul is writing of, this letter may primarily concern salvation.