Abby is a Caltech science or humanities graduate student/employee, who Rajesh Koothrappali and Sheldon met when they went to the University Mixer. She is good friends with Martha, and becomes Raj's date for a night.
As Leonard and Howard are both off on a double date with Penny and Howard's blind date (Bernadette) (their first date), Rajesh Koothrappali feels lonely, and suggests to Sheldon that they go out and have some fun. After much persuasion and actually giving away his Green Lantern lantern, Sheldon agrees to go with Raj. At the University Mixer, they meet Abby and Martha, where Martha instantly became interested in Sheldon's limited edition Green Lantern lantern and power ring.
All four of them head back to Sheldon's apartment, where they are seen playing Rock Band. Raj yet again is interested in going out with Abby, but she will only agree to hang out with him if Martha can come along. Raj bribes Sheldon with his Incredible Hulk hands signed by legendary comic book writer Stan Lee.
As Sheldon and Martha engage in conversation, Abby and Raj make out with each other. Sheldon says that its late and time to go to bed to which happily Martha agrees with. To Martha's surprise Sheldon says good night and leaves her. Later Martha knocks on Sheldon's door and says that "they're getting busy in the living room". She asks if she can hang out in Sheldon's bedroom hoping for coitus with Sheldon. Sheldon accepts, and immediately leaves saying "I'll go sleep in Leonard's room" leaving a very surprised Martha. She hasn't been seen or mentioned again since this incident. ("The Psychic Vortex")