A galactic trader offers an exchange of goods. He has an eye for beautiful things, and has hyperdrive technology the Alphans are interested in, but he is only really interested in one thing: Maya, who has no interest in him. Taybor eventually shows his true colors, kidnapping her. Koenig gives her a clue which she uses to attempt a successful escape, and Taybor, a "sore loser," revokes the exchange of all the small things, and takes back the big one: the hyperdrive information.

Plot

Small, shiny items appear throughout Alpha, and several people are stunned by handling them. Almost immediately, and with a flourish, a colorful spaceship appears, captained by a trader named Taybor. The devices were gifts, of which the Alphans did not know the proper use.

He appears in Command Center, and tries establishing a rapport, all while eyeing Maya a lot and lavishing compliments on her beauty.
Taybor, John, Helena, Tony, and Maya talk over a meal, and the Alphans discover he has a "jump drive" which operates via hyperspace. The Alphans at first hope he can transport them to a habitable planet, then back to Earth. In later discussion, however, both ideas fall through.
Taybor offers Koenig a tour of his ship, the S.S. Emporium. John discovers Taybor is a collector of beautiful artwork and objects. Taybor's ship vanishes, taking Koenig on a short surprise demonstration jaunt into hyperspace, much to the Alphans' consternation. The ship returns, and John asks for Taybor's price in trading for knowledge of the jump drive. The price: Maya. Koenig refuses, of course: "Maya is not mine to give away." Taybor refuses any further trade, but Koenig thinks of trading jump drive plans, for a mannequin-like model of Maya with a robotic voice, one which will "always be beautiful.... Never grow old." Taybor accepts.
A separate trade of smaller items, between Taybor and various Alphans, overseen by Tony and Maya, is completed. At the end, Taybor creates a ruse with a pendant and some perfume which separates Maya from the other Alphans, and hypnotizes her via a device, allowing him to kidnap her to his ship. When the other Alphans discover this, Koenig demands Taybor return Maya. He acceeds^, and she reappears in CC, but explodes; "she" is the robot.
Maya shakes off the hypnotic influence of the pendant, throwing it aside, just as Taybor takes the ship into hyperspace. She demands her release. After a confrontation, she ends up in a glass cage, but Koenig conveys a key piece of information to Maya, which she uses to transform into a "slatternly woman" who repels Taybor to the point he relents and releases her. A sore loser, he reverts the exchanges, including taking back the jump drive primer diagrams.

Details

Taybor's initial gifts gave the stunned individuals hours of blissfully recalling forgotten memories. Unverified: several Alphans later trade for more such devices?
Besides the prior point, there are other unpleasantries over Taybor's arrival. He asks for permission to land, does not identify himself, is refused, but his ship appears and lands anyway, triggering defensive posture on Alpha's part. Taybor then just transports himself into Command Center. He immediately has weapons turned on him, but in turn makes a tank appear for a few seconds, its gun pointed at Alpha, before revealing it an illusion, and after a few more words that it and he are harmless, everyone calms down.
At the dinner, where Helena is in a casual dress (?), and Maya is in her Psychon dress, Taybor is drinking a lot, and carousing as well. He tries to surreptitiously put a move on Maya, which she firmly rejects. He later mentions the jump drive, before turning almost incoherent, then collapsing, unconscious. Helena: "Drunk as a trader."

Alphans' sudden hope for a return to Earth is dashed when the Alphans uncertain and vague descriptions of location (long established that Alpha long since lost track of the position of Earth) do not equate to any location reference system Taybor is familiar with. However, while initially talking about a possible return to Earth, Taybor notices Maya's less enthusiastic reaction, and finds out her world is destroyed, which seems to provoke some thought in him.
After Maya shakes the hypnotic effects of the pendant, and demands her release, Taybor offers to marry her, and travel the galaxy with her. She refuses, and then transforms. He is surprised, but deals with it almost immediately, and despite a chain of direct transformations, ends up back as herself, this time caged.
Taybor, with Maya kidnapped (but now back to full awareness), has jumped to hyperspace and broken communications with Alpha. However, Koenig, previously suspicious of Taybor's motives, had attached a limpet transmitter with subspace(?) capabilities onto the ship, and now uses it to convey a critical piece of information about Taybor to Maya, which she uses to create a way to offend Taybor to the point he releases her.
Maya claims she "locked" herself in the "slatternly" form. This is a bluff on Maya's part. That she has a time limit on molecular transformation is clearly a fact of which he is unaware.

Quotes

Tony, to John, regarding Taybor accepting a 3-D "copy" of Maya: "A wax work dummy with a computer voice? He's not right in the head."
Taybor, after the robot Maya explodes in CC: "Did..did you think I'd settle for a copy, skipper? I..I only collect originals!"
John, to Maya, based on observations he has made about Taybor: "Taybor surrounds himself with things of beauty, that's why you're there." It is essentially an ad hoc coded signal, an statement John knows Maya will be able to interpret, create a solution from, and hopefully act on, without clueing Taybor into any specifics that he may be able to guard against.
Maya/slatternly, to Taybor: "I will be the judge of where I want to be; and I want to be back on Alpha."