Is there any way how to install just ADB without whole SDK?

Yes you can

Installing ADB in windows without Download Android SDK

1. Firstly, you'll need a program that can partially download contents of zip files from the internet.
2. Once that's set up, go to the SDK download page and grab the link to the SDK.
3. In the zip file, navigate to "android-sdk-windows\tools"
4. From there, select only "adb.exe", "AdbWinApi.dll" and "AdbWinUsbApi.dll"
5. Download.

Source: http://twigstechtips.blogspot.in/2011/07/android-downloading-adb-without-sdk.html

It is now available officially from Google as a separate tool. You can download it from here SDK Platform Tools Release

I got adb.exe and the required .dll files from: http://adbshell.com/downloads

Very minimalistic, but does exactly what it needs to do.