Spoiler alert: This post is part of an in-depth discussion of Sign of the Unicorn by Roger Zelazny, which will inevitably reveal key plot points. I recommend reading the book first. It's short, I promise.
Corwin made good his promise to overthrow his brother Eric and take the throne of Amber—at least, indirectly. Eric died in battle with the creatures of the black road as they besieged Kolvir, the mountain on which the palace of Amber sits. Dara, Corwin's supposed great-grandniece, was revealed as one of these dark creatures, and she threatened the destruction of Amber before disappearing.
A week later, Corwin is the de facto ruler of Amber. However, his brother Caine was murdered by another being from the black road, apparently intending to frame Corwin for the deed. His brother Random encountered these creatures before, so Corwin met privately with him and demanded some answers.
Chapter 2 is told from Random's point of view as he tells Corwin that story. He was visiting a Shadow where he could pursue his hobbies—namely, drumming, gliding, gambling, and women—when he suddenly receives a communication from his missing brother Brand, who is being held prisoner in a tower somewhere in Shadow. Random can see enough of the landscape in the vision to attempt to travel there.
He finds the tower in the far reaches of Shadow, surrounded by floating, orbiting rocks, and guarded by a giant, luminous warden in the form of a snake. Random attacks but fails to kill the snake, so he is unable to rescue Brand. He is chased away by the wounded beast and several other creatures from the tower. He defeats the snake beast by causing it to be struck by one of the flying rocks, but the other beings pursue him through Shadow. He kills several of them, but cannot lose them.
Random flees to Earth and California, where he is ambushed by the creatures in a bus terminal before he escapes by plane to New York and Flora's mansion, still pursued by the remaining six creatures. Here, he meets Corwin, and they dispatch his final pursuers, as we know from Nine Princes in Amber.
During the escape from the tower, Random communicates with Julian, who informs him that Oberon is missing and presumed dead. This left a vacancy on the throne that Eric wants to fill. Corwin has already fired us in on this aspect of Amberite family politics, of course. However, Corwin was also presumed dead by his siblings, thought to have been killed by Eric, rather than (as we know) exiled to Earth. Random was actually surprised that Corwin answered Flora's phone in New York, and assumed that it was him who had sicced the Shadow things on him. We already know that's not what happened. Possibly, a traitor in Amber has it in for the Amberites.
The tower where Brand is imprisoned is "somewhere where the shadows go mad." Like literal shadows, it looks like the farther away they emanate from Amber, the more indistinct Shadows become. The floating boulders around the tower imply that the normal laws of nature break down. Does this mean that Amber and less remote Shadow worlds follow a consistent set of physical laws—beyond, say, which materials are combustible or not?
Speaking of Shadow, up until now only the Amberites have been shown with the ability to manipulate reality and move between universes. The notable exception is Dworkin, the designer of the Pattern and Trumps, who doesn't have the innate ability that the Amberites do; but somehow, he has figured out how it works. Yet now we've discovered that these Shadow freaks also know to pursue Random through Shadow. Who are these guys, and who is using them to get at … Corwin and his allies?
"Childe Random to the dark tower came," remarks Random about his approach to the tower. This is an allusion to the Robert Browning poem, "Childe Roland to the Dark Tower Came," published in 1855 in his collection Men and Women. Clearly Zelazny's setting for the chapter was inspired by this poem. A few years later, Stephen King took more direct inspiration from "Childe Roland" for his Dark Tower series, even naming the protagonist Roland.
Corwin already knew Brand was alive, since Corwin successfully contacted him in Nine Princes. However, he never learned his location, while Random did. Corwin also knows Oberon is alive. I would guess that some kind of rescue missions are coming up.