Romans 16:20 (Brief Notes)

Greek-ὁ δὲ θεὸς τῆς εἰρήνης συντρίψει τὸν Σατανᾶν ὑπὸ τοὺς πόδας ὑμῶν ἐν τάχει. Ἡ χάρις τοῦ κυρίου ἡμῶν Ἰησοῦ μεθ' ὑμῶν.

Syntax-Definite article (ὁ) occurs with the substantive word, "God" (θεὸς). The word for God is the subject nominative; continuative δὲ is the postpositive word here. On the other hand, Johann Albrecht Bengel thinks δὲ is adversative in this case (i.e., "but").

τῆς εἰρήνης is possibly a subjective genitive or could be a descriptive genitive.

συντρίψει-future active of συντρίβω ("shatter," "crush" or "bruise").

"The term συντρίψει, shall bruise, is evidently an allusion to the ancient promise, Genesis 3:15, which—strange to say—is referred to nowhere else in the N. T." (Frédéric L. Godet)

"There is an allusion to Genesis 3:15, though it is doubtful whether Paul found anything there answering to συντρίψει. The LXX has τηρήσει." (The Expositor's Greek Testament)

τὸν Σατανᾶν-accusative singular masculine of Σατανᾶς.

ὑπὸ τοὺς πόδας ὑμῶν-"under your feet." Accusative; an expression also signifying that the subject has total control over the subordinate entity (LN 37.8).

ἐν τάχει-"speedily"