Into the Shadow Web Caverns is chapter 7, part one, of the Legacy of the Damned.
Continuing their way to the Frozen Throne, Arthas, Anub'arak and his loyal undead arrive at the ancient Nerubian kingdom of Azjol-Nerub. Arthas has the undead corpse of Sapphiron stay behind and guard them from any followers, since they could not bring it in.
As they make their way underground, they encounter a branch of dwarves which had made the underground tunnels their home. The dwarves recognize Arthur as the traitorous prince that "killed" Muradin Bronzebeard (Muradin had survived Arthas' betrayal, but was presumed dead), and blow up a bridge to stop Arthas' advance.
With Anub'arak's help, Arthas made his way around the detour, and encountered Nerubians who still resisted the Lich King's attempts to subjugate them, and were hostile to the dwarves. The Undead eventually made their way to the end of the first sublevel, where they encounter Baelgun Flamebeard, the leader of the dwarves in Azjol-Nerub. After several heated words between Baelgun and Arthas, he fought the Undead with his remaining dwarves, only to fall in battle.
After the battle, Anub'arak notices that the dwarves were scared of something in the lower tunnels, and advises caution as it is most likely still down there.