So, this list of textbooks is very close to the list of textbooks that the University of Washington uses (the UW has one of the top Atmospheric Science programs in the nation). I've also included some supplementary material that I've felt helpful in my study. You can find a list of course webpages at http://www.atmos.washington.edu/academics/classes.shtml. Most of the graduate level courses use a lot of course notes (one example is http://www.atmos.washington.edu/~dennis/552.index.html).
I'm also adding some planetary science textbooks as I feel that these can really enhance one's understanding of Earth's atmosphere. For a full understanding of the material, you should also study some physics, chemistry, earth science, and get a working knowledge of MATLAB + some computer science and basic electrical engineering.