As already mentioned, the best place to start is your drawing skills. Life drawing. Lots of it.. 2 hours per session doing 30 second gestures LOL (omg how we got slammed with this in animation school). Looking at photographs isn't the same as working from a live model. What these gestures teach you is this: proportion, anatomy, movement, foreshortening, perspective
These are the foundations of 2D animation. Being able to quickly reproduce a drawing with the same proportions. Maintaining mass is probably one of the trickiest parts of 2D animation. It requires a hella lot of flipping and refining and an eye for continuity errors.
Squash and stretch is a good principle to understand also.
These days, the majority of animation is cut-out 2D animation an 3D animation. It's beneficial to understand the foundation of classical animation to be able to apply the most eye-pleasing way to make something move. Animation in general uses a lot of exaggerated movements to communicate what's going on to the audience.
It's been so long since I've studied it myself. I do recall my life drawing instructors highly recommending Hogarth's books for anatomy studies. I'm afraid I can't make additional suggestions to what's already been said.
These pretty much apply to 3D animation as well. Except the drawing part.. it's pretty much manipulating a puppet. Cut-out 2D animation is kidna the same if you're using skeletons.Anyhoo, good luck and don't give up! Animating is some pretty intensive labour....
UNO. Take the time to be able to do flip books and stuff, they teach you patience and pacing. You don't need fancy bound paper. I used my english books since we never had to give them back. Of course almost any book will do.
DOS. Take time to learn about color, people are more pink then they are yellow and putting someone in a dark room will make them kinda yellow, or if they are in a dark place looking at a phone, a blue/purple light will shine on them. Theire is many great stuff on deviant art about it.
TRES. Get the animation book by Kit Layborne. This book is very 90's style, but it gives you great ideas and uses actualy animation examples. Plus it shows lots of different types. It is what got me into stop motion animation. But it talks about round-abouts for characters, to the different types of walk styles. It has stuf on storyboarding and cameras..
QUATRO. Buy books about different types of styles of art. Christopher Hart has hands down best books on manga. Plus you can find him here on DA. For more comic types- stan lee has a few books. The better thing about stan Lee is that he is big in the buissness. Who has not heard of spiderman? Plus what I like about his books is he also talks about the back end of things too. Since every animation has characters- character mentor by Tom bancroft is good. Art books will only do good and make it easier to go back to basics.
CINCO. I stress the importance of backgrounds. DOO ITT, Even if it is a bunch of gray smears, its better than nothing!
CES. Every animation is a story, so read up on writting and dialouge. A good how to guide is here: [link]