Where to learn algebraic analysis

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).

[KKK] "Foundations of Algebraic analysis" is not easy for beginners, I highly recommend to read A. Kaneko's "Introductions to Hyperfunctions", and Morimoto "An introduction to Sato's Hyperfunctions". And there is another one "Fundamentals of Algebraic microlocal analysis" by Struppa and Kato, also very good. [SKK]/LNM 287 is another classical book, but very hard to read. Please try to search M. Sato, M. Kashiwara, P. Schapira, and else.