Two books are required reading for all animators:
The Illusion of Life by Frank Thomas and Ollie Johnston
The Animator’s Survival Kit by Richard Williams
If you can’t find The Illusion of Life, John Lasseter sums up the important parts in his SIGGRAPH paper on “The Principles of Traditional Animation Applied to Computer Graphics,” but I prefer the explanation given in The Illusion of Life.
Optional books:
Timing for Animation by Harold Whitaker and John Hales
Cartoon Animation by Preston Blair
The Animator’s Workbook by Tony White
Character Animation Crash Course! by Eric Goldberg
Animation Tips and Tricks, Volumes I and II by Shawn Kelly
Thinking Animation: Bridging the Gap Between 2D and CG by Angie Jones and Jamie Oliff
Reading is good and all, but getting better at animation also requires feedback and critique from mentors and peers. Consider putting your work-in-progress online and asking people for feedback on how to improve your animation. Sometimes having fresh eyes looking at your project can give you a better perspective on what you’re missing.