Eddard 1
The Starks receive the three hundred plus party that is the King's Entourage. Eddard recognizes amongst them the queen's brothers - Jamie Lannister of the King's Guard and Tyrion Lannister, a dwarf known also as the imp. However he is at a loss for the man leading them - - the king. Instead of the strong and burly warrior that he knew in his youth, the king has become fat. Eddard notes that he has not seen the king for nine years, since Balon Greyjoy's rebellion.
The Starks and Baratheons greet each other and after introductions are conducted, King Robert Baratheon asks Eddard (affectionately called Ned) to take him down to his crypts. Cersei, the queen, complains that they can wait, they have been riding for so long but the king will hear nothing of it.
Ned takes the king down to where his immediately family are buried: his father Rickard Stark, elder brother - Brandon Stark, and sister - Lyanna Stark. Ned reflects on how his brother was strangled on the order of Aerys Targaryen days before he was supposed to marry Cateyln Tully, Ned's current wife. Robert pays his respects to Lyanna, who was his betrothed. He complains to Ned that she shouldn't be buried in a crypt such as this, a beauty like her deserves better. Eddard responds that she is of the north and that this is her place. Furthermore Eddard reminds Robert that he was with her sister when she died and that she pleaded to be buried with her father and brother. Eddard also secretly remembers a promise made to her and how once he assured her he would honor it, how all fear left her eyes. This he does not bring up to Robert.
Robert states how he vowed that he'd kill Rhaegar Targaryen, son of the mad king, for what he did to Lyanna. He laments he could only do so once; he kills him a thousand times in his dreams.
The topic changes to the late Jon Arryn, both men fondly remember their time together at the Eyrie. Robert tells Ned that Jon's sickness came swiftly. He seemed the pinnacle of health only a fortnight before his death. Robert says that Jon's wife (and Catelyn's sister) Lysa Arryn has been driven almost mad with grief. She has taken her young and sickly son, Robert Arryn from King's Landing to the Eyrie. This is problematic for Robert since Tywin Lannister, his father in law, had already agreed to take the boy on as a ward. Eddard is skeptical of allowing Tywin to care for the boy, but Robert dismisses him. They have a short discussion regarding the status of the Warden of the East...a position that Jon Arryn held which Robert has decided his sickly son shall not inherit...at least until he comes of age. However soon Robert brings up the true reason he has come to the north. To offer Eddard Jon Arryn's old position: The Hand of the King. This is an incredibly powerful position, second only to the king itself and is the last thing Ned wants. Finally Robert states he intends to betroth his son, Prince Joffrey, to Ned's eldest daughter Sansa Ned asks for some time to mull this over and feels a sense of foreboding.
Commentary
We technically meet a lot of really important characters this chapter. But I'm not talking about any of them save for one since they don't do anything. This chapter is pretty much dedicated to introducing the King of Westeros. I think a king deserves an entire chapter to himself, no?
A good portion, through Robert's almost lustful description of the food and women of the south also serves as a dichotomy of the north and...well everything else. From what Robert says, compared to the north it's a virtual paradise. Of course it's really no surprise that Robert is over-exaggerating.
The discussion about the Arryns is important in that it sets up this books framing device. All you really need to get from it though is that Jon died suddenly, Robert (Jon's son...damn a lot of the characters have the same name) is sickly, and Lysa is a bit off her rocker. Rereading it though I did find the plot points about Tywin acting as Lil' Robert's ward and King Roberts decision to find a new Warden of the East interesting (if minor enough that I forget them) given what happens later.
We also learn early on that Theon Greyjoy is a ward since his father rebelled against Robert a few years back. Sort of ironic given how Robert himself was the rebel not long before that. Anyway this chapter was mostly about exploring the friendship between Robert and Eddard and setting up some big plot points. Not much else to see here.