TOS Season 2 Episode 1 Amok Time

They introduce the concept of Pon Farr, which isn’t exactly our favorite part of Vulcans, although it’s best portrayed in this episode. They also establish that Vulcans are both logical, but also sort of religious, which is an interesting part of Vulcans. This episode showcases the deep friendship between Kirk, Spock and Bones.

Plot

Spock, the first officer of the USS Enterprise, begins to exhibit unusual behavior and requests that he be granted leave on his home planet Vulcan. Captain Kirk and Chief Medical Officer Dr. McCoy, having witnessed one of their friend's outbursts, agree and Kirk diverts the ship to Vulcan. En route, Kirk receives orders from Starfleet to travel to Altair VI to represent the Federation at the inauguration ceremony for the planet's new president. Though Kirk instructs the crew to set course to Altair VI, Spock secretly changes course back to Vulcan. Kirk confronts Spock, who claims to have no memory of ordering the course change.
Kirk orders Spock to Sick Bay, where McCoy finds evidence of extreme physical and emotional stress, a condition that will kill him within eight days if not treated. Spock is forced to explain that he is undergoing pon farr, a condition male Vulcans experience periodically throughout their adult life, and that he must mate or die. Kirk contacts Starfleet to request permission to divert to Vulcan but is denied. Kirk disobeys orders, believing that saving the life of his friend is more important than his career.
At Vulcan, Spock invites Kirk and McCoy to accompany him to the wedding ceremony. He explains that Vulcans are bonded as children so as to fulfill the pon farr commitment and that T'Pring is to be his mate. T'Pring arrives with Stonn, a pureblood Vulcan, whom she prefers to Spock. T'Pau, a matriarch renowned as the only person ever to refuse a seat on the Federation Council, prepares to conduct the ceremony. However, T'Pring demands the kal-if-fee, a physical challenge between Spock and a champion she selects. To everyone's surprise, she chooses Kirk instead of Stonn. Spock begs T'Pau to forbid it as Kirk is unaware of the implications, but T'Pau leaves the decision to Kirk; another champion will be selected if he refuses. Kirk accepts the challenge, only to learn that it is "to the death."
The two begin combat with lirpa, a traditional Vulcan weapon. Kirk is challenged by Spock's strength and agility, even in his current state, as well as the thinner atmosphere of Vulcan. McCoy convinces T'Pau to allow him to inject Kirk with a tri-ox compound to offset the effects of the Vulcan atmosphere. The battle continues, with Spock eventually garroting Kirk with an ahn'woon. McCoy rushes to Kirk's body and declares him dead, and requests immediate transport back to the Enterprise.
Spock renounces his claim on T'Pring but not before demanding an explanation from her. She explains that she feared losing Stonn in the kal-if-fee. By choosing Kirk, T'Pring would be assured of having Stonn in some capacity regardless of the outcome: If Spock was the victor, he would release her from the marriage (for having made the challenge in the first place), and if Kirk had won, he would not want her either. Spock, now free of the pon farr, compliments T'Pring on her flawless logic and returns to the Enterprise, warning Stonn that "having is not so pleasing a thing after all as wanting."
Aboard the ship, Spock announces his intent to resign his commission and submit himself for trial for killing Kirk, when he discovers Kirk is alive and well in sickbay. McCoy explains that the injection he gave Kirk was a neuroparalyzer drug that merely simulated death. Asked about what followed, Spock states that he lost all desire for T'Pring after he thought he had killed Kirk. Kirk then learns that Starfleet, at T'Pau's request, has belatedly given the Enterprise permission to travel to Vulcan