I read somewhere that Genesis "feels" and reads differently than the rest of the Torah, because God is not yet the savior and law-giver of Israel. God is working with people and making connections, so to speak, accompanying the Hebrew ancestors as they begin a history in the land promised to Abraham.
Chapter 1-11 is a block of material prior to the Bible's main story that begins with Abraham. Of course, we first study the two creation accounts: the "priestly" narrative of 1:1-2:4a and the "Jahwist" narrative of 2:4b-3:24. I've also read how the Genesis stories "demythologize" other ancient Near Eastern stories. For one thing, the creation story has a covenantal purpose: Genesis 1 links over to Exodus 31:12-18, where the Sabbath is part of God's eternal covenant with Israel, based in God's own rest from creative activity. We Gentiles, mulling over the literalness or symbolism of the seven days, miss the very key point of the Sabbath (not so named in Genesis) that becomes Israel's "sanctuary in time" (Heschel).
Other aspects of "demythologizing": Even though God seems anthropomorphic, walking in the garden, not much is made of this in the narrative, and there is certainly no "birth" account of the deity, nor does Eve function as a fertility goddess or demigod like Asherah. There is a "trickster" entity who deceive the first couple, which introduces sin into God's creation and separation from the deity, although notice that God helps the couple make clothing before they leave the garden!
A theme that we find in much literature, inspired by the Bible story, is the way children continue the sin of their parents, and of course Cain takes the almost careless sin of his parents and multiplies its horror, killing his own brother. The genealogies that follow his story show the one way that human beings were faithful to God---being fruitful and multiplying. Otherwise, without getting into theological theories of free will vs. original sin, the narrative moves along human moral decline. The Noah stories, which evidence an editing of the J and P sources, anticipate later biblical themes: God's eventual judgment against sin, and also God's demand for purity and purification.
The remainder of the Genesis 1-11 block is filled with genealogical information of the descendants of Noah moving out into the world. (Here is a map that sorts it all out: http://www.bible-history.com/maps/images/genesis_shem_ham_japheth.jpg) I read somewhere (I need to take better notes!) that the narrative of Acts, intentionally or not, follows in reverse order the Table of Nations in showing how the Holy Spirit came to people around the ANE and eastern Roman Empire. Here, however, the genealogies include a narrowing of focus: to a particular family, that of Abram (Abraham).
The Abraham stories---which as I say is the crucial beginning of the biblical story---fill 12:1-25:18. I think I'll take these notes through chapter 22. At the end of chapter 11 and into chapter 12 and following, we meet Abraham and his family, learn of God's call and promise to the patriarch, and read of some of his adventures: his gaining of property during a sojourn in Egypt, during which he's caught in a well-intentioned lie; his separation from his nephew Lot and his flock; his rescue of Lot during an intertribal conflict; and his meeting with the king of Salem, Melchizedek, who worships and serves the one God. This last story connects with the history of Jerusalem, which we'll read about much later, and also with Jesus, who is praised by the author of Hebrews as a priest like Melchizedek.
There is ugliness and sorrow in the Abraham stories. The expulsion of Hagar and Ishmael is tragic (21:-34), though it gives the Lord a change to bless both son and mother. Hagar, in fact, has more of a role in praising and naming God than any woman in the narrative up to this point. We also have the narratives of Lot, of Sodom, and the incest perpetrated by Lot's daughters. There is a subtle point in the narrative that the children of the daughters are ancestors of Moabites and Ammonites, two of Israel's enemies in later centuries.
There is beauty, though, in the way Abraham openheartedly beseeches God to spare the city if there be a few righteous people to save. It is a classic story of how God may respond to prayers of intercession on behalf of persons about whom we care, for whom we hope for God's compassion and help.
The Harper's Bible Commentary (p. 99) notes that 20:1-22:24 are stories of the Elohist source (that makes use of the general name Elohim for God, rather than the sacred name YHWH, but is not the Priestly source which also uses Elohim). The commentator writes that the stories have the same structure: "God instructs Abraham to initiate a course of action that will involve mortal danger to another family member (Gen. 20:12; 21:12; 22:2); the patriarch obeys (20:1-2; 21:14; 22:3); the threatening situation is about to be realized (20:1, 18; 21:16; 22:9-10); and God intervenes to prevent the expected outcome (20:6-7, 17; 21:19-20; 22:11-13)" (p. 99). Little wonder that Abraham becomes the great paradigm of faith in three major world religions---the Abrahamic religions---because of the extraordinary commands of God and his extraordinary, often wordless and distressing obedience.
I remembered a post from a couple years ago on my now-seldom-updated "Changing Bibles" site: the Pentateuch, another name for the Torah or the first five biblical books, has interesting theological and textual issues, revealing contrasts of view points and challenging insights. Some of the issues pertain to Genesis' relation to the other books: http://changingbibles.blogspot.com/2015/05/the-pentateuch.html
In the Jewish tradition, the weekly passage from the Torah is called the parshah, each with a name coming from the Hebrew text. The corresponding reading from the Prophets is called the Haftarah. Here are the readings (from the Judaism 101 site), with the haftarah in parentheses indicating the Sephardic readings:
Parshah Torah Haftarah
Bereishit Genesis 1:1-6:8 Isaiah 42:5-43:11 (Isaiah 42:5-42:21)
Noach Genesis 6:9-11:32 Isaiah 54:1-55:5 (Isaiah 54:1-10)
Lekh Lekha Genesis 12:1-17:27 Isaiah 40:27-41:16
Vayeira Genesis 18:1-22:24 II Kings 4:1-4:37 (II Kings 4:1-4:23)