These are books that I have actually read since having the stroke and consider worthwhile for those actively recovering from brain damage, their carers, and anyone experiencing depression. There's some books here that are also more general exercise-related tomes, which are of value to everyone.The Brain That Changes Itself, by Norman Doidge, has essential implications for sufferers from stroke. You can recover. It helped me understand how my brain was working to recover, and to make that effort as worthwhile as possible.
Twists and Turns, by Matthew Mitcham. This autobiography is a great read. If you have ever doubted that depression is somehow real, Mitcham was the best in the world at the 10m platform dive, and still suffered. Depression is common after a stroke, with good reason, and there are few better examples of why we need treatment. (Review here.)
My Year Off, by Robert McCrum, still a good read about the experience of having a stroke, although I wept less, and Kazuo Ishiguro never came to visit me in hospital. Weirdly, I was at the same prep school as McCrum, but some years later.
Anatomy of Movement, and Exercises, by Blandine Calais-Germain. These two volumes are a great reference for what muscles we have, and which exercises work them. Remember that stroke itself damages the brain, not the nerves or muscles, so working the muscles and generating the signals is how the brain can re-learn to use our bodies. (Review here.)
Stretching Scientifically, by Thomas Kurz. Once you get past the obsession with doing the splits (sure a 70-year-old dude may be able to do the splits, but it's still gross), this is an excellent and thorough look at stretching. Understanding the science behind what works and what doesn't has saved a lot of wasted time and effort.
(As I read books that I think are worthwhile, I'll add them here.)