Stephen Crawford was a physics graduate student, working on a thesis concerning multiple dimensions. One evening, his thesis disappeared from reality and became an energized mental construct in his mind, which he unleashed to travel to the fantasy world of Mecond.
On Mecond, Stephen was mistreated by the locals and unable to recharge the mental construct to return to Earth. He eventually made his way to the local Wizards' Guild and impressed them with his mathematical knowledge. Learning elementary spells and making friends with another apprentice named Rurth, he 'captured' Rurth who became a second mental construct, which Stephen was able to 'unleash', summoning the apprentice as a champion to do his bidding.
Eventually, Stephen learned an ‘identify’ spell and started to understand these mental constructs as cards that could be powered and unleashed to return what they represented to reality. He accidentally captured a ghoul he'd studied, the Wizards' Guild itself, Blargh, a nasty innkeeper who had robbed him when he first arrived, and a magic sword owned by Rurth's aristocratic father.
Stephen began to understand that he captures things when he understands them well and has strong emotional feelings about them. He accidentally captured Shomos, a druidess he'd begun a romance with, while hunting for battery cards (cards that power other cards). This allows him to charge the dimensional travel card that brought him to Mecond and leave that dimension.
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Avin, the first other dimensional traveler Stephen meets, duels the man from Earth shortly after his arrival at his pocket dimension, a personal reality made up of all the cards he's captured. Stephen loses the duel, which costs him Shomos' card. Avin demands an outrageous price for her return. Dimensional travelers who have previously met can track one another through 'contacts' in their pocket dimensions. This lets them communicate, trade, or duel with one another. It also shows every dimension the other traveler visits, which allows Stephen to travel to new dimensions.
Stephen, Blargh, and Rurth explore Mecond, Earth, Avin's dimension Riowiver, and a dimensional hub for travelers, Stredath. Stephen joins a club, The Malachite Club, for travelers in Fortune, the main city in Stredath and learns more about his abilities. Through this club he becomes friends with Feyrith and Falco, two other travelers. Falco takes Stephen to Phodynn, a dimension that's been ravaged by dimensional travelers, and Stephen begins to understand the possible impact of his abilities.
After assembling the large ransom Avin demanded and securing Shomos' return, the group decides to steal a statue, named Adam, from Avin, antagonizing the other traveler. Avin begins harassing Stephen on Mecond and Earth.
Shomos, upset at having been captured by Stephen, learns what he has discovered about the nature of dimensions and dimensional travelers. She agrees to help him navigate his new situation.