I want to learn flash animation.
Are there any good resources I could study and which program should I use?
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One of our Lecturers at university provides all his teaching material on his website so that anyone interested in learning Flash can go through the same tutorials / leture notes that someone studying the course for real.
The website is: http://www.gavinsim.com/teaching/index.html
Image Manipulation and Interactive Flash Programming - CO2711
Audio and Motion Graphics - CO2711
Multimedia Development - CO4740
Course Material - CO4741
There is a bit of Overlap between the courses but i found that this was an excellent place to start and built it up from there.
The lectures assume availability of Flash CS4 and AS3
One option is to follow the part of Flex in a Week (scroll down a bit to see it) that is about animation.
Flex in a Week is a series of 47 video tutorials and 26 exercises and is licensed under a Creative Commons Attribution-Noncommercial license.
These ones are probably interesting for you to check and study:
Software? Flash, really. Is a industry standard. And even when HTML 5 becoming strong,(perhaps long way before it can really compete, I don't know) I expect Adobe making something to output html5, they have the tool dominating the market already. For a worker, it's important this matter, is what you'll be asked to be skilled at, like always in these cases :)
As alternatives, but I really recommend mastering Adobe's Flash, you can have a look at ToonBoon, Koolmoves, AnimeStudio (before was Moho from LostMarble, it allowed setting bones in 2d...) But these are mostly (koolmoves a bit more general) just for the character animation part, Flash makes many more things.
But really, Adobe Flash CS5 all the way.
EDIT -- Ouch, forgot some key resources:
flashkit.com (and really great forums here)
There are many more, but with all this you have a lot of work already :)