When I try to save the K2 category settings I get this error: [1064] You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 3.

K2 v2.10.1

I can't tell much about this. The error should probably indicate more. Can you paste the full error redacting the path up to Joomla's root folder?

Where can I find it?

Set error reporting to maximum in Joomla's Global Configuration and check again if more information is reported while installing K2.

I try "maximum reporting" - no more info =(
I get this error when i save the category settings (K2 -> Categories - > "My category" and press [Save & Close]

Do you also have SIGPro installed? If so, is it up to date?

SIG PRO is not installed

Re-install Joomla from the Joomla Update component and then re-install K2 as well.

Your method didn't help me. =(

I'm sorry but I can't possibly know what's wrong with your site. You're the first to report such an issue. If it's not a corrupt Joomla/K2 installation, it may be some system plugin causing issues. Start disabling your 3rd party "system" or "k2" type plugins one by one to see which one affects your category save action.

Ok, thx you.

Please let us know if you solve your issues. It may help others as well in the future.