Verses 37-39 are one long sentence in Hebrew and in Revised Standard Version. Most translators will need to divide the section into several shorter sentences (see the models in Good News Translation and Contemporary English Version).
He loved your fathers: this refers to their ancestors, particularly the patriarchs, Abraham, Isaac, and Jacob. “Love” is often described in a figurative fashion; for example, “his heart [or, liver] yearned for” or “his heart [or, liver] felt very warm towards.” For fathers see 1.8.
Chose their descendants after them: the people of Israel, when Yahweh decided to make them his own. God’s love for them and his choice of them are linked also in 7.7-8 and 10.15. The plurals their and them follow the Samaritan, Septuagint, Syriac, Targum, andVulgate; the Hebrew Text has the singular “his descendants after him,” which Hebrew Old Testament Text Project prefers. The committee suggests two interpretations of the Hebrew: (1) “their posterity after each of them”; (2) “his posterity after him” (that is, the posterity of Jacob). A meaningful translation of the first interpretation will come out the same as the translation of the text of the ancient versions. It will be helpful in certain languages to state directly that Yahweh chose the Israelites; for example, “he chose you, their descendants, to be his own people.”
Brought you out of Egypt: the same verb that is used in verse 20.
With his own presence: literally “with his face,” meaning that Yahweh did this himself, without an intermediary. The Septuagint, like modern translations, has “he led you out himself.” Good News Translation has “he himself brought…” (and see Exo 33.14).
By his great power: this probably goes with the previous words (Revised English Bible, Bible en français courant, New Jerusalem Bible, New Jewish Publication Society’s Tanakh); for example, “So the LORD used his great power and personally brought you out of Egypt.”
Quoted with permission from Bratcher, Robert G. and Hatton, Howard A. A Handbook on Deuteronomy. (UBS Helps for Translators). New York: UBS, 2000. For this and other handbooks for translators see here .