Although for the ancient Israelites Adam and Eve are not particularly prominent figures, Christian theology values them enormously. We value them because in Adam we see a type of Christ, a parallel drawn in particular by St Paul in the epistle to the Romans, chapter 5. I will not for now discuss that passage in Romans - I will get to it in due time, but the typological parallels that are relevant will be drawn. I will also only note the differences with Genesis 1 where relevant.
"Then the LORD God formed man [Hebrew adam] from the dust of the ground [Hebrew adamah], and breathed into his nostrils the breath of life, and man became a living being." (v. 7)
The author is using a play on words here between "adam" and "adamah", the word for "man" and the word for "ground." This is a sort of humbling message, specially after Genesis 1 where we get the importance of being in the image of God and having dominion over the earth. This foundational truth is important to grasp, and we are reminded of it every year on Ash Wednesday when we have the priest draw the cross in ashes on our foreheads and say much the thing that is said in this verse.
"The LORD God took the man and put him in the garden of Eden to till it and keep it. And the LORD God commanded the man, 'You may freely eat of every tree of the garden; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall die." (vv. 15-17)
Having established that God is in no way indebted to man, we see that still God gives to him everything he needs - he asks only that man refrains from the tree of the knowledge of good and evil, for his own sake. If man eats from the tree, then on that very day, he will die. This is a losing of the divine life, not of the earthly life - for us creatures, to have the divine life requires the earthly life, the biological life, but it is certainly distinct. It is completely false to transpose the statement and say that biological life means one has divine life. St John's gospel uses the word life in this way, as the divine life, since even those condemned still have life, in some sense.
Summary of verses 18-22: The man names all the animals, but none are quite a suitable partner, so God makes woman from the man's rib. Then we read:
"Then the man said,
‘This at last is bone of my bones
and flesh of my flesh;
this one shall be called Woman,
for out of Man this one was taken.’
Therefore a man leaves his father and his mother and clings to his wife, and they become one flesh. And the man and his wife were both naked, and were not ashamed." (vv. 23-24)
God continues in his providence, having already given man everything he needs physically, he makes woman, the companion of man, who together can be mutually fulfilling. An incredible mystery is found here, because St Paul (or whoever wrote the epistle to the Ephesians) is going to take this and make it apply to the relationship between Christ and the Church. Let us make one point very clear: this relationship sets up the mystery, but it is not in itself part of the mysterious oneness of the body in marriage - the man and the woman here were the same flesh beforehand also.
"And the man and his wife were both naked, and were not ashamed." (v. 25)
I think this verse has some key information about the nature of sin, too, and also helps us understand what St Paul writes in the epistle to the Romans about the law and sin. I will comment on this, however, in relation to what happens after they eat of the fruit, when I comment on Genesis 2.
A take home point:
So far, everything is written so as to be thought of as perfect. This is, quite literally, paradise, the garden of Eden. In the context of the book of Genesis, we are meant to think of it this way - but we're also meant to have a problem. We, as human beings that live in the real world, have absolutely no experience of God in this way, or of the perfection of paradise. Both Genesis 1 and Genesis 2 have problems which the Enuma Elish, the epic of Gilgamesh, Sumerian myths and any other number of creation (and soon, flood) stories avoid easily: we have a perfect God, yet the world seems far from perfect. Throughout the next 10 chapters in particular, but throughout Genesis as a whole, the writer is going to have to treat the problem of evil in a way no previous religions had to. The reason for evil is going to have to be something other than God himself - and we shall get to what the writer says in Genesis 3.
 I use type in the typological sense.
 Differences abound, but since Genesis 1-11 does not attempt to write history in the conventional sense, it is not a matter of particular importance.
 I don't wish to poke too much fun at my young Earth creationist brethren, but they seem to miss that humans were made from the ground if and when they say things like "evolution destroys the dignity of humans by making them a product of the natural world." The theory of evolution may not be found explicitly in the Bible, but the idea that we are made from the most earthly of things - literally, the earth of the ground, certainly is.