The field moves quickly. So much of the material dates quickly. Joining a professional association such as IEEE or IFR and regular reading of publications – magazines and journals – is essential.
The Handbook of Robotics is a massive book. But is amazingly good at giving a broad sweep of the field.
Probabilistic Robotics by Sebastian Thrun et al. gives an excellent grounding in statistical and machine learning methods for robotics.
For people starting out in robotics I recommend the brilliant LEGO MINDSTORMS by Laurens Valk. It provides practical ways to teach and inspire the next generation of roboticists.
I also recommend people read some inspiring science fiction to get motivated! You can’t go past Isaac Asimov and his classic I, Robot.