I wonder if there is a possibility to assign the permission for only one space to an external user? I want him to see only this space, nothing else.

[Julia Wester [Wittified]]

He will need to be a registered user (you can't separate him from others if he is logging in as anonymous.

It will be possible to do what you want if his username is not in any group allowed access to other spaces AND you allow access for him to this particular space via a group he is in or as an individual user.

Please see this page for details on how to assign permissions: https://confluence.atlassian.com/display/DOC/Assigning+Space+Permissions

Just note –  if you're allowing access for confluence-users on other spaces and he is in confluence-users, you will have to change that (either change the group you're using for permissioning or somehow remove him from confluence users).