Why does the Torah begin this Pasuk with the letter "Vav"?
Rashi: Hashem was saying to Avraham, "I have entered into a covenant with you, and it is up to you to maintain that covenant by performing the B'ris Milah!"
What is the meaning of Bris Milah, and why was Avraham chosen to first fulfill this Mitzvah?
Maharal (Tif'eres Yisrael Ch. 19, p. 60): The word Orlah means a covering or a blockage. 1 The generations prior to Avraham were under the domain of Teva (the natural order since Creation), and nature separated between them and Hashem. Avraham was the first to emerge from this blockage; earning a connection to Hashem and a covenant with Him. Therefore, a Bris is performed on the eighth day, for the number eight means being above nature [which was created in seven days].
"How great is Bris Milah; thirteen covenants were sealed upon it! [I.e. the word "Bris" is mentioned thirteen times in this section of the Torah]" (Nedarim 31b). What does this signify?
Rosh (to 17:13): This corresponds to the 13 Midos through which the Torah is expounded. The Mitzvah of Milah (like Shabbos and Tefilin) corresponds to the entire Torah.
Maharal (Chidushei Agados Vol. 2, p. 5, to Nedarim 31b): The Orlah is a Kelipah ("shell") that separates Hashem from a person, and its removal completes the covenant with Hashem. By definition, an absolute covenant can only be made with one party, and not two. Avraham is known as "unique" (Yachid), 1 and 13 is the Gematriya of "Echad" (one).