I have been studying categories, sheaf cohomology and complex analysis (the basics since I know just a little). Then recently I tried to find out more about algebraic analysis and these microlocal stuffs, but I couldn't find any introductory material.
I know about the books and papers by Kashiwara and they are a little advanced for me. (However, I have never seen Foundations of algebraic analysis since this book is not so easily found.) Any material, lecture notes, etc are welcome.
Here's a link to Foundations of Algebraic Analysis by Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura. It's not available from, new, from Amazon, but is available as a used book for purchase.
You might want to search a university library for the text, to see if it meets your needs before considering purchasing it. If not available at your library, you might want to request it through inter-library loan.
I'd suggest Googling Mikio Sato, who is credited for having started the field of Algebraic Analysis.
There is also an entry on Wikipedia which may give you some directions for further searching: Algebraic Analysis, with links to entries on the territories that overlap with the field.
Here is a webpage with links to online books and lecture notes in some of the sub-fields you mention (e.g., algebraic geometry).