Does any one know when the last book from the Inheritance trilogy is coming out?

Answer 1

Like the others have said, release information it hasn't clarified as of yet. It is beleived to arrive either later this year or the next.
However, i doubt it will be far away. because Random House has permitted the Book 3 Excerpt to the general public via the internet, instead of the restrictive Eldest Special Edition.
I have included this Exceprt;
Enjoy ;)

Empire Excerpt by Christopher Poalini

Saphira kneaded the soil beneath her feet. Let us be off! Leaving their bags and supplies hanging from the branch of a juniper tree, Eragon and Roran clambered onto Saphira’s back. They wasted no time saddling her; she had worn her tack through the night. The molded leather was warm, almost hot, underneath Eragon. He clutched the neck spike in front of him—to steady himself during sudden changes in direction—while Roran hooked one thick arm around Eragon’s waist and brandished his hammer with the other.

A piece of shale cracked under Saphira’s weight as she settled into a low crouch and then, in a single giddy bound, leaped up to the rim of the gulch, where she balanced for a moment before unfolding her massive wings. The thin membranes thrummed as Saphira raised them toward the sky. Vertical, they looked like two translucent blue sails.

“Not so tight,” grunted Eragon.
“Sorry,” said Roran. He loosened his embrace.
Further speech became impossible as Saphira jumped again.

When she reached the pinnacle of her jump, she brought her wings down with a mighty whoosh, driving the three of them even higher. With each subsequent flap, they climbed closer to the flat, narrow clouds that extended east to west.

As Saphira angled toward Helgrind, Eragon glanced to his left and discovered that, because of their elevation, he could see a broad swath of Leona Lake some miles distant. A thick layer of mist, gray and ghostly in the pre-dawn glow, emanated from the water, as if witchfire burned upon the surface of the liquid. Eragon tried, but even with his hawklike vision, he could not make out the far shore, nor the southern reaches of the Spine beyond, which he regretted. He had not laid eyes upon the mountain range of his childhood since leaving Palancar Valley.

To the north stood Dras-Leona, a huge, rambling mass that appeared as a blocky silhouette against the wall of mist that edged its western flank. The one building Eragon could identify was the cathedral where the Ra’zac had attacked him; its flanged spire
loomed above the rest of the city, like a barbed spearhead. And somewhere in the landscape that rushed past below, Eragon knew, were the remnants of the campsite where the Ra’zac had mortally wounded Brom. He allowed all of his anger and grief over the events of that day—as well as Garrow’s murder and the destruction of their farm—to surge forth and give him the courage, nay, the desire, to face the Ra’zac in combat.

Eragon, said Saphira. Today we need not guard our minds and keep our thoughts secret from one another, do we?
Not unless another magician should appear.

A fan of golden light flared into existence as the top of the sun crested the horizon. In an instant, the full spectrum of colors enlivened the previously drab world: the mist glowed white, the water became a rich blue, the daubed-mud wall that encircled the center of Dras-Leona revealed its dingy yellow sides, the trees cloaked themselves in every shade of green, and the soil blushed red and orange. Helgrind, however, remained as it always was—black.

The mountain of stone rapidly grew larger as they approached. Even from the air, it was intimidating.

Diving toward the base of Helgrind, Saphira tilted so far to her left, Eragon and Roran would have fallen if they had not already strapped their legs to the saddle. Then she whipped around the apron of scree and over the altar where the priests of Helgrind observed their ceremonies. The lip of Eragon’s helm caught the wind from her passage and produced a howl that almost deafened him.

“Well?” shouted Roran. He could not see in front of them. “The slaves are gone!”

A great weight seemed to press Eragon into his seat as Saphira pulled out of her dive and spiraled up around Helgrind, searching for an entrance to the Ra’zac’s hideout.

Not even a hole big enough for a woodrat, she declared. She slowed and hung in place before a ridge that connected the third lowest of the four peaks to the prominence above. The jagged buttress magnified the boom produced by each stroke of her wings until it was as loud as a thunderclap. Eragon’s eyes watered as the air pulsed against his skin.

A web of white veins adorned the backside of the crags and pillars, where hoarfrost had collected in the cracks that furrowed the rock. Nothing else disturbed the gloom of Helgrind’s inky, windswept ramparts. No trees grew there among the slanting stones, nor shrubs, nor grass, nor moss, nor lichen, nor did eagles dare nest upon the tower’s broken ledges. True to its name, Helgrind was a place of death, and stood cloaked in the razor-sharp, sawtoothed folds of its scarps and clefts like a bony specter risen to haunt the earth.

Casting his mind outward, Eragon confirmed the presence of one of the slaves, as well as the two people whom he had discovered imprisoned within Helgrind the previous day, but to his concern, he could not locate the Ra’zac or the Lethrblaka. If they aren’t here, then where? he wondered. Searching again, he noticed something that had eluded him before: a single flower, a gentian, blooming not fifty feet in front of them where, by all rights, there ought to be solid rock. How does it get enough light to live?

Saphira answered his question by perching on a crumbling spur several feet to the right. As she did, she lost her balance for a moment and flared her wings to steady herself. Instead of brushing against the bulk of Helgrind, the tip of her right wing dipped into the rock and then back out again.

Saphira, did you see that!
I did.

Leaning forward, Saphira pushed the tip of her snout toward the sheer rock, paused an inch or two away—as if waiting for a trap to spring—then continued her advance. Scale by scale, Saphira’s head slid into Helgrind, until all that was visible of her to Eragon was a neck, torso, and wings.

It’s an illusion! exclaimed Saphira.

With a surge of her mighty thews, she abandoned the spur and flung the rest of her body after her head. It required every bit of Eragon’s self-control not to cover his face in a desperate bid to protect himself as the crag rushed toward him.

An instant later, he found himself looking at a broad, vaulted cave suffused with the warm glow of morning. Saphira’s scales refracted the light, casting thousands of shifting blue flecks across the rock. Twisting around, Eragon saw no wall behind them, only the mouth of the cave and a sweeping view of the landscape beyond.

Eragon grimaced. It had never occurred to him that Galbatorix might have hidden the Ra’zac’s lair with magic. Idiot! I have to do better, he thought. Underestimating the king was a sure way to get them all killed.

Roran swore and said, “Warn me before you do something like that again.”

Hunching forward, Eragon unbuckled his legs from the saddle as he studied their surroundings, alert for any danger.

The opening to the cave was an irregular oval, perhaps fifty feet high and sixty feet wide. From there, the chamber expanded to twice that size before ending a good bowshot away in a pile of thick stone slabs that leaned against each other in a confusion of uncertain angles. A mat of powder-gray scratches defaced the floor, evidence of the many times the Lethrblaka had taken off, landed, and walked about thereon. Like mysterious keyholes, five low tunnels pierced the sides of the cave, as did a lancet passageway large enough to accommodate Saphira. Eragon examined the tunnels carefully, but they were pitch-black and appeared vacant, a fact he confirmed with quick thrusts of his mind. Strange, disjointed murmurs echoed from within Helgrind’s innards, suggesting unknown things scurrying about in the dark, and endlessly dripping water. Adding to the chorus of whispers was the steady rise and fall of Saphira’s breathing, which was overloud in the confines of the bare chamber.

The most distinctive feature of the cavern, however, was the mixture of odors that pervaded it. The smell of cold stone dominated, but underneath it, Eragon discerned whiffs of damp and mold and something far worse: the sickly-sweet fetor of rotting meat.

Undoing the last few straps, Eragon swung his right leg over Saphira’s spine, so he was sitting sidesaddle, and prepared to jump off her back. Roran did the same on the opposite side.

Before he released his hold, Eragon heard, amid the many rustlings that teased his ear, a score of simultaneous clicks, as if someone had struck the rock with a collection of hammers. The sound repeated itself a half-second later.

He looked in the direction of the noise, as did Saphira.

A huge, twisted shape hurtled out of the lancet passageway. Eyes black, bulging, rimless. A beak seven feet long. Batlike wings. The torso naked, hairless, rippling with muscle. Claws like iron spikes.

Saphira lurched as she tried to evade the Lethrblaka, but to no avail. The creature crashed into her right side with what felt to Eragon like the strength and fury of an avalanche.

What exactly happened next, he knew not, for the impact sent him tumbling through space without so much as a half-formed thought in his jumbled brain. His blind flight ended as abruptly as it began when something hard and flat rammed against the back of him, and he dropped to the floor, banging his head a second time.

That last collision drove the remaining air clean out of Eragon’s lungs. Stunned, he lay curled on his side, gasping and struggling to regain a semblance of control over his unresponsive limbs.

Eragon! cried Saphira."

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Cheers ;)

Answer 2

The date hasn't been set yet.

Answer 3

It's still being written, so there is no date set...