What books about development methodologies(agile?) and management, planning you can recommend?

Of course as stated above "scrum from the field" +1
Very simple and easy.
\r
Then we read the Manifesto agilemanifesto.org/
meditate, read again.
meditate, read the 12 principles
meditating, looking for books of all fathers
starting with Kent Beck bookz.ru/authors/kent-bek/ekstrema_365.html
Direct enter in the search queue (a list in manifest) and all the download and buy.
Why?
Because it is described very much, but after reading still remains a lot of questions like:
* "it really works"
* "what about the money"
* "how to make"
* "I want to, but the boss(the client) asshole does not understand"
...
It is still necessary to figure out how to adapt it to yourself, the team, the mentality.
Sure, everyone decides this for themselves in their own way.
\r
Communicate with colleagues in the madness.
\r
I want to understand deeper?
Then Wellcome to Japan — TPS (TOYOTA production system)
Lean manufacturing
I am deeply convinced that many of the principles of agile came from American institutions adapted TPS
\rwww.labirint.ru/authors/38718/
start from here www.labirint.ru/books/59079/
then www.labirint.ru/books/54441/
\rwww.labirint.ru/books/108142/

All the advice from scrumtrek
\rscrumtrek.ru/products/
the podcast is in unitology for beginners the most.

Maybe you will be interested in Getting real.