Kirk must determine whether a visiting Shakespearean actor is really the dreaded Kodos - the executioner of Tarsus.
I pay little attention to people who dump on this episode as lacking in aliens, space battles, and other devices. 1960s television actually stretched every once in a while - to some people's pleasure and other's disdain. Here, it's meant as an exploration of human psyche and psychosis. So this is a revealing episode, exploring Kirk's past, his willingness to think about its causes, and the relations of a father and daughter.
The father/daughter relationship is the strength and weakness of this installment. Kodos is a little too broadly drawn, his murdering sin could have been a little less all-encompassing than ordering the death of half a planet and still work. That aside, there is a nice sense of a mystery as attempts are made on the Captain's and Riley's life. McCoy, on the other hand seems to be not too tightly-written, he changes opinions on Kodos a number of times.
All this leads to the fascinating character of Lenore, daughter of the infamous Kodos. I like the idea, but am a bit repelled by Barbara Anderson's screeching, whining, and half-crazed delivery. Even watching in the earliest days of 70s syndication it weirded me out and distracted me. Still, there is a sad sense of tragedy here (as befits a Shakespeare theme), and parts of the musical score are good enough to be included in "City on the Edge of Forever".