In another video a therapist is shown chanting "I love you," to Giffords, who struggles to chime in with the word "you." It is an occasion for cheers.
The videos also show the importance of music in Giffords' recovery process. Because of the damage to Giffords' language pathways in the brain, from the very beginning of rehabilitation therapists would use songs as a different way to retrain her brain.
Gifffords would sing a variety of songs, everything from Tom Petty's "Free Fallin'" to "Tomorrow" from the musical "Annie." The songs also offer a chance for moments of levity and fun in what could often be grueling rehab sessions.
Kelly tried to extend that light mood as much as possible for his wife's recovery, posting a "No Crying" sign on the door of Giffords' hospital room. During therapy, Giffords cracked jokes when she could.
"Gabby, you sit in a, what?" the speech therapist asks Giffords in another home video.
"Spoon. Chair. Goofball," she says quickly, laughing.
"Did you just call yourself a goofball? Goofball Giffords?"
"Yes," Giffords answers, laughing.
Another time, when they'd been joking about hyphenated names, Kelly walked into the room and Giffords looked up at him.
"Giffords," she said, her therapist and husband looking at her in confusion. "Mark Kelly-Giffords."
"Kelly-Giffords? No. I'm not changing my name. Ain't happening," Kelly said, to everyone's laughter.
That positive attitude, which Kelly said was his favorite thing about Giffords when they met, helped her learn to walk and speak again. Though Giffords was severely injured, and is only just now beginning to step back into public life, she and Kelly are considering a run for reelection next year -- if she can. It's a decision, he says, Giffords will make by May 2012 -- the filing deadline.
In the last page of the book, the only chapter written in her own voice, Giffords says she wants to return to Congress and to work for the American people if she can.
"I will get stronger," she writes. "I will return."
Kelly, always the supporter, says he thinks she can recover enough to serve once again.
"She doesn't give up," Kelly says. "If that's what she wants, that's what I want for her. You know, I think she has the right to a chance to recover. She was elected by a lot of people who voted for her in Arizona. When she knows she's ready, she'll make the decision."
Kelly's faith in his wife's recovery is a sentiment shared by many of the doctors who have worked with Giffords.
"I think she'll continue to recover… throughout her lifetime," says Dr. Nancy Helm-Estabrooks, Giffords' Speech Pathologist and Professor Emeritus, Western Carolina University. "I'm not putting any cap on her. I can't begin to think far she might go."
Kelly also hopes that within the next year Giffords and he will be able to make a decision about whether to attempt once again to have a child together.
"Gabby and I hoped that 2011 would be the year we finally could have a child together," Kelly wrote. Giffords had been undergoing fertility treatments with a doctor in Washington, with whom she had an appointment for the second week in January, just days after the shooting.
Kelly said he still hopes that they could have a child together and they are keeping many options open, including surrogacy.