Boasting

Galatians 6:14 NASB
But may it never be that I should boast, except in the cross of our Lord Jesus Christ, through which the world has been crucified to me, and I to the world.

What contrast word begins this verse?
What is being contrasted with what? (See Galatians 6:13.)
What does Paul mean by "boast"?
When I looked up "boast" in Strong's, there were no listings for "boast," so I looked up these two verses in the KJV, which is the version that Strong's is based on. Here they are:

Galatians 6:13-14 KJV
13 For neither they themselves who are circumcised keep the law; but desire to have you circumcised, that they may glory in your flesh.
14 But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world.

So, what is meant by "glory"?
The Strong's number for both of these verses is G2744. Paul used the Greek word "kauchaomai," which means to vaunt (in a good or bad sense). What does vaunt mean? Webster's defines it as "to make a vain display of one's own worth or attainments, to call attention to often pridefully and often boastfully."
Who are those who are insisting on circumcision calling attention to?
Who is Paul calling attention to?

What does Paul say that the cross of our Lord Jesus Christ has accomplished?
What does he mean by "crucified"?
The Strong's number is G4717. Paul used the Greek word stauroo, and it means "to impale on the cross; figuratively to extinguish (subdue) passion or selfishness."
So what is Paul saying that the cross of Christ has done to Paul's relationship with the world?
Where in Galatians has Paul previously mentioned himself or believers being crucified?
Read Galatians 2:20 and 5:24.
So, if Paul were to boast, why do you think he would boast about the cross of Christ?
If you were to boast, what should you boast about?