This is the second pilot of the series, and as such is technically the first appearance of James T. Kirk, as well as Sulu and Scotty. Everyone is wearing the same style uniforms as featured in "The Cage" rather than the more familiar ones.
The plot is classic man-becomes-god (featured in "Charlie X" and numerous other franchise episodes), featuring Kirk's good friend and Starfleet Academy classmate Gary Mitchell. The status of this episode among fans is sufficient that when it was still believed that Benedict Cumberbatch was playing someone other than Khan in Star Trek Into Darkness, it's Gary Mitchell who was the leading contender.
Although the series was famously episodic, where you could miss any episode and not be missing anything when you caught the next one, many of the individual installments tended to resonate on the backstories of the characters. This tendency was already seen in the previously broadcast "Man Trap," which featured McCoy. Although Kirk is a classic example of someone who lives for the moment, his past continually comes back to revisit him throughout the series, in the form of old classmates surprisingly often. Mitchell sets that precedent, certainly, as well.
It's odd to think that the famous original cast took so long to nail down. Spock was in "The Cage" and "Where No Man," and of course Scotty and Sulu in the latter as well. Sulu is designated an astrophysicist, rather than in his more familiar role as helmsman. There are one-time characters in the episode who fill some of the other traditional roles, such as yeoman and ship's doctor. If you're looking for Chekov, though, you must keep waiting until the second season!
I tend to trust Gene Roddenberry's instincts as he worked on his Star Trek pilots. Both "Cage" and "No Man" remain some of the strongest, most distinctive episodes of the series, both of them using the captain (Pike in the first one, Kirk in the second) as a sounding board for a story that ends up much bigger than them, whereas other episodes tended to make the captain bigger than the story, thus diminishing the impact of the story (and ultimately making the series too trivial for viewers to care enough about to keep on the air for more than three seasons; fans love the characters, but if they just float from adventure to adventure, their weightlessness becomes apparent). The network thought Gene was trying to be too cerebral, but his approach to science fiction was clearly ahead of its time.
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