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I've been looking all over the website, but I can't find the location of the source code to download it. I am interested in understanding GATK more in depth and possibly developing walkers for it. Thanks.
There's a link to our Github source code repository on the Downloads page. The button is white and says "Github".
Be sure to check out the Developer Zone documentation as well. Some of it is a little out of date but it should help you get to grips with the basic structure of walkers and how they interact with the engine.