Becoming a Supple Leopard
Start here in your journey through mobility. It's half textbook teaching, half reference. It'll make you rethink your daily habits.
Simple and Sinister
The reference for starting kettlebell training, written by the master who brought kettlebells to the Western world. Quite possibly the best conditioning for rock climbing, for power and injury prevention (especially shoulders).
If you're female, this is an absolute must-read. It details how to adapt your training, eating, and life to work with your physiology and hormones. It's ludicrous more of this information isn't mainstream since the world's half female, and a shame that most disseminated information is based on men's physiology. For example, during your luteal phase (post-ovulation, pre-menstruation), estrogen and progesterone spike, and your body becomes catatonic (breaks down muscle rather than builds), so intense exercise can actually be detrimental to athletic growth.
Need climbing-specific training ideas? Here ya go. Written by Alex Megos' trainers.
Make or Break
Nagging climbing injury you want to rehab yourself? Wondering what's too little to do? This book goes over common injuries and when to take a full break vs. work through your injuries. It's written by a Brit, and has way better info than we typically get in the US.
The Crack Climber's Technique Manual
The 3D illustrations are mind-blowing. I've never read a single climbing book as good as this one in describing technique. After being a boulderer for 8 years and having ACL reconstruction, I started in other climbing venues. This book was wow.
The Roll Model
Goes hand-in-hand with Supple Leopard. Goes over how and where to roll your soft tissue for muscle pliability. Great for post-surgery rehab!
Search Inside Yourself
Mindfulness is such the craze nowadays. This book was totally worth the read, though, especially during those half-depressed days when you're going through injury/surgery rehab. The author has an awesome dry humor.