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Rayleigh is shown to possess great mastery of Haki, and made use of all three types while teaching Luffy about them, and training him in the basics.
Rayleigh has mastered Haoshoku Haki (Conqueror’s Haki) to the extent that he can render a specific target completely unconscious. He is able to do this without adversely affecting anybody else near the initial target. He disabled an entire hall room of hostiles with this power, save for the Kid Pirates and Heart Pirates.
Only very strong and determined individuals can resist from being knocked unconscious. One of Trafalgar Law’s crewmen was very close to being knocked out, and even Law and Eustass Kid were sweating slightly after enduring the blast.
Busoshoku Haki (Armament Haki) allows Rayleigh to create a force similar to an invisible armor around himself. Rayleigh has the ability to bypass the powers of a Devil Fruit user, touching the “substantial body” beneath whatever protection the fruit provides as seen when he used Busoshoku Haki to kick and redirect an attack from Admiral Kizaru.
He was also seen using it to deflect a giant elephant’s foot and also hurting Luffy with a Haki-imbued flick while teaching him the basics of Haki. Overall, Rayleigh’s immense proficiency in Busoushoku Haki allows him to use it for devastating offense. He is also able to harden certain parts of his body or objects, as shown during his training with Luffy.
Kenbunshoku Haki (Observation Haki) can allow Rayleigh to sense the emotions and nature of others. It appears that it is also possible for the user of this Haki to sense the strength of others. This was shown when Rayleigh used this Haki to sense that there were five hundred creatures on Rusukaina who were stronger than Luffy at that time. Rayleigh also used Kenbunshoku Haki to dodge an elephant’s attack without directly seeing the elephant.
The strength and mastery Rayleigh has over this kind of Haki is also shown by the fact that he can sense people all over the island he is currently on while most people can sense only in their immediate vicinity.