A Rider's sword was an elegant blade made specially by the elven smith Rhunön, for each Dragon Rider, should they choose to wield one. All of the blades were crafted out of brightsteel and each blade was the color of its bearer's dragon. As Brom describes in Eragon, the riders swords will never break and will never rust. Rider's swords are shown to cut through iron with ease.
When Eragon I first established the Riders, they may not have used swords forged by Rhunön, for at that time they were merely ambassadors between the elves and dragons: however Rhunön mentioned, "when Queen Tarmunora asked me to forge the first of the Riders' swords, it was brightsteel I used", so perhaps the elf-smith did indeed make the swords for the entire order of the Riders. In Brisingr, Oromis said to Eragon that Rhunön-elda is one of the oldest living elves, even elder than the dragon riders themselves, and that she made all dragon riders' blade.
The elf smith, Rhunön, discovered a new type of steel that she found in a meteorite. She later christened the steel "brightsteel", for the unusual brilliance of the metal. When she began molding the steel into new blades, she discovered the steel was extremely strong and flexible. Rhunön took the brightsteel and constructed the first Rider's blade for Eragon I. Over time, the brightsteel became harder and harder to find. She found one last horde in the forests of Ellesmera and with that steel, she made Zar'roc for Morzan, Undbitr for Brom, and five other unknown blades. The only surviving Riders and their dragons were The Forsworn, Brom, Galbatorix and Galbatorix's new dragon, Shruikan, which he stole with the help of Morzan, one of the thirteen members of the Forsworn. After the destruction of the Riders and rise of the Broddring Empire, Rhunön, motivated by despair and disgusted by the acts of the Forsworn, swore an oath in the Ancient Language to never again create a weapon of destruction. Thus, only a few swords existed at the time of the Rider War: Zar'roc, in the possession of Murtagh; Naegling, Oromis' sword; Brisingr, Eragon Bromsson's newly forged sword; and Vrangr, Vrael's sword that was taken by Galbatorix. Additionally, an unknown number of swords are held in Galbatorix's "collection", the unknown sword held by Cuaroc in the Vault of Souls and two were held by elven families: Támerlein and Arvindr.
When Rhunön constructed the swords of the Dragon Riders, she fit a gem into the hilt that matched the color of the blade. The Dragon Riders discovered that the jewels in the hilts could hold a nearly endless amount of energy. The energy stored into these gems could help a dragon and his or her Rider whenever and wherever their energy was becoming drained. But gems were not just used in swords, they were used in the Belt of Beloth the Wise and also in the ring called Aren, which belonged to Brom, who later passed it onto Eragon. Zar'roc had a great ruby, Undbitr had a sapphire, Naegling had a yellow diamond, Támerlein had a great emerald, Arvindr's blade was purple as was the jewel in its hilt (most likely an Amethyst, but possibly a purple variety of Sugalite or Zircon, or maybe a purple Diamond or Goldstone) Brisingr had a sapphire as well and Vrangr had a clear diamond in it.
Each Rider's sword was the same color as their dragons. Zar'roc was colored red, the same color as Morzan's dragon. When Brom took the sword after slaying Morzan, he gave it to Eragon to begin his sword training, but then Murtagh stole his sword.
Many fans have wondered why the Riders choose swords, instead of lances and spears, which would have been more productive. The most likely reason is that the Riders were not meant to fight full-scale battles. Another reason could be that since they didn't expect to fight other Riders, they could leave the attacking to their dragon and defend with a sword which is much easier than defending with a spear. They were to be keepers of the peace, not warriors. A sword would be more suitable for law enforcement, as that's all a Rider is supposed to do. When riding on the back of dragons, a sword would be easier to handle and keep track of. It is also possible that appearance played a part - the Riders in their heyday were highly respected, with as much standing as aristocrats and monarchs. Moreover, they stood for universal peace. Swords were the traditional weapons of choice to wear as a symbol of station (aristocracy wore swords or daggers to most official events), therefore, a man (or elf) with a sword at his belt might not be immediately identified with a warrior in public. On the other hand, a man with a six-foot spear or a stack of throwing weapons was quite sure to. However, as imposing a magic wielding Dragon Rider might be with any of those, it might also be one of the most efficient weapons to use, as a pommel stone (usually a gem of some sort and necessary for balancing out a sword) could be used as a magic container, whereas a spear or axe would leave little room for a gem.
Forging and materials
All Rider swords, from the founding day of their order, were forged by the elf smith Rhunön, one of the greatest smiths of all time. A unique material was used for all of these swords and for them only: brightsteel, a metal created by Rhunön from meteoric iron, remains of a star that fell in Du Weldenvarden millennia ago. By the time Eragon requested Rhunön forge him a Rider's sword, there were virtually no more known fragments of the star left: still, hundreds, if not thousands of swords must have been made, for each Rider had his own. Scabbards were made of wood and grips were leather, wire, and wood.
All the swords Rhunön forged, except for Brisingr, were made through a lengthy process consisting almost exclusively of manual work - Rhunön was loath to use magic in her craft unless absolutely necessary. Rhunön usually constructed an ore smelter specifically for the occasion, doing so with bricks and clay and no magic. Then, she would spend a day or more refining the ore, depending on the quality of the given piece. When the ore was pure, Rhunön chose an assortment of harder and softer pieces and from these forged the spine of the weapon (from the softer steel, to make the weapon flexible and able to absorb kinetic shock) and what would become the blade (from the harder steel, for obvious reasons of sharpness and durability). All of the pieces were folded and hammered back out several times, making the steel of the sword layered, giving it superior physical properties. In addition, the blade steel was twisted together from two layered rods. Then, the blade and the spine were forged together while hot and meticulously crafted into the desired shape. The entire process would normally take days to weeks. Rhunön only worked by night to be able to judge the current state of the heated metal by its color. During the entire forging process, Rhunön chanted an endless stream of spells over the metal she was simultaneously working, most of which presumably only she knew, giving the metal properties no amount of additional enchanting could grant a normally-forged blade.
At this stage the weapon was black, rough and unadorned. Rhunön would continue for weeks and etching more decorative designs into the blade, filing, scraping and polishing it and finally incorporating the gemstone into the hilt, fashioning a grip, a scabbard, as well as giving the sword its color. The latter was done by unspecified means, probably magic using the scales of the Rider's dragon as a basis for the coloring. Blade, hilt and scabbard of a finished sword were all richly decorated and displayed various tones of the dragon's scale color. When used, the blades of the Rider's gave off an iridescent sheen, like that of a butterfly's wings. Upon being presented with the blade, the Rider was asked to name his new weapon and as a final touch, the corresponding symbol was magically inscribed upon the blade and scabbard.
Once finished, a Rider's sword was easily a weapon without equal in all of Alagaësia, except for others of its kind. Moreover, the swords were custom-made, their dimensions and parameters personalized to the Rider who would wield them. Thus, while each sword was different, each was the perfect weapon for its owner. This was simultaneously something of a drawback, however, preventing the successful use of a Rider's sword by anyone other than its original owner. The fact that both Eragon and Murtagh were able to wield Zar'roc without much difficulty seems to actually have been a very rare occurrence, especially in Eragon's case, as he was not directly related to Morzan. Though it should be noted that Eragon learned how to wield a sword while using Zar'roc in the first place, which may have influenced his fighting style.
Christopher Paolini stated the forging process of a Rider's sword was adapted from the traditional Japanese sword making techniques.
Existing Rider Swords
Zar'roc, the crimson blade of Morzan, was christened "misery" in the ancient language. It was originally presented to Morzan from Rhunön, but after the Fall of the Riders, Morzan and Brom dueled each other near Gil'ead. Morzan fighting in self-defense, Brom fighting for revenge. In the battle between the Forsworn and the Dragon Riders, Morzan killed Brom's dragon Saphira. After Brom slew Morzan and his dragon, he claimed Zar'roc as his own and returned to Carvahall. Later, after Brom discovered that Eragon was the new Rider, he gave him Zar'roc to use in their travels. Eragon later discovers his old friend, Murtagh, who had been kidnapped earlier by Galbatorix's bidding, caused the second dragon egg to hatch for him, making him a Rider. With his red dragon, Thorn, Murtagh and Eragon fought each other over the Burning Plains. With Murtagh being the victor, he claimed Zar'roc from Eragon as his rightful inheritance, as he was the older "brother" of the two.
Zar'roc remained in Murtagh's possession as he went into self exile.
Oromis's golden blade, which was the same color as his dragon, Glaedr, was named Naegling. On the day that Oromis revealed his and Glaedr's survival of the battle between the Forsworn and the Dragon Riders, he was killed by Murtagh after he lost his sword in battle. It was most likely added to Galbatorix's collection of Riders' swords, or it may have been recovered by the elves.
Eragon's sword, Brisingr, was a miracle in itself. Against the odds, Eragon found the greatly needed brightsteel when it was believed that no more ore existed. What's more, Rhunön found a way around her oath to never forge another weapon. She did this by reaching out to Eragon with her mind and used his body to forge the sword. Brisingr was in her own words the best sword she had ever made, despite the fact Rhunön and Eragon forged the sword in less than a day, when the process usually took several weeks. The blade itself was a rendition of Zar'roc with a slightly thinner tip, the blade was also slightly shorter to allow easier use in cramped spaces and longer handle to allow for stronger blows when he didn't have a shield in his left hand. The scabbard was a beautiful, rich, dark blue like the scales on Saphira's back. At the end of the scabbard was a beautifully carved cap of brightsteel shaped like a leaf, as well as a stylized vine design at the mouth of the scabbard. The blade's color was a lighter shade of blue, like the scales on Saphira's throat. The hand-and-a-half hilt was made of black wood. The beautiful curved crossguard was unadorned but magnificent all the same. And lastly, the pommel of the sword, was a sapphire of undenied beauty held in place by four claw shaped ribs. The sword was named thus because the pattern Eragon saw on the blade reminded him of the first spell he used when he first used magic and so the sword was christened Brisingr. Interestingly, whenever Eragon spoke the word "brisingr", the sword would burst into blue flames. Tested by Rhunön, Eragon was the only one who could call upon the flames of Brisingr. It was also theorized by Rhunön that it was because Eragon was part of the making of the blade and because Eragon had discovered its true name.
Brom's sword before the fall of the Riders. It was aquamarine blue, the same color of Saphira I. Since a Rider's Sword is near impossible to destroy, it was probably in Galbatorix's possession. At one point in Brisingr, Eragon asked Rhunön where to find Brom's sword, since Murtagh was using Morzan's sword, it would have been fitting that Eragon used his own father's sword. However, the elf smith said that it would take too long to find the sword. The sword may have been recovered after Galbatorix's death if it was in his collection of Riders' swords.
Támerlein was the emerald green sword of the deceased Elven Dragon Rider Arva. He was killed defending Ilirea by the Forsworn Kialandi. He gave his sword to his sister Naudra to defend herself. She escaped to Ellesméra along with another dragon and Rider, who was then killed. It resided in Ellesméra in the care of Lord Fiolr, Naudra's mate. It was a treasure of the house of Valtharos. It was green, with an emerald set into its pommel. A column of glyphs adorning the crossguard spelled "I am Támerlein, Bringer of the final sleep." Eragon tried it out after losing Zar'roc, but he rejected it. He did so because of the fact that it did not fit his hand, was too heavy to hold (therefore not allowing Eragon to strike fast enough), and was made for someone with a different fighting style than his own, as well as because Saphira did not like the conditions created by Lord Fiolr. He disliked that Fiolr would not allow him to keep it indefinitely. Fiolr had a gleam in his eye when Eragon told him he (Eragon) would not take the sword, probably because he held Arva in high esteem and in his eye, this showed that Eragon was not worthy of Arva's sword; that, or he was loathe to part with such a sentimental item. After Fírnen hatched for Arya, Rhünon reworked Támerlein to better suit her grip.
Arvindr was presumably the sword of an elven rider (possibly Thuviel) that was an unknown shade of purple. It resided in the elven city of Nädindel.
Vrangr was the sword of Vrael and was taken from him by Galbatorix after Vrael's defeat. Vrangr is described as white and bleak. Vrangr ("awry") is the name given by Galbatorix to the sword he uses. Its blade, hilt and crossguard are pure white and the jewel in its pommel is "as clear as a mountain spring". The sword belonged originally to Vrael and its name was Islingr ("Light-Bringer"). Galbatorix stole the sword from Vrael's corpse after he killed him and gave it a name he found "more appropriate".