Move everything from your b2evolution folder up one level to your root, then change the $baseurl in your conf/_basic_config.php file to reflect the new fact (meaning remove the "/b2evolution" from it).

I moved everything from b2evolution up one level to the root and changed the $baseurl. It works! Thank you very much.

For people who have got the same problem:
My blog contains only a few posts, so for me there is no problem with existing permalinks. But you should consider this when changing the path in this way. Im sure you can solve this problem with mod_rewrite.

Another aspect is, that you get a complex root directory with many files and folders in it.

Do this if you changed URL/folder/etc in an existing site (which I recently learned):

Options +FollowSymlinks
RewriteEngine On

RewriteBase /

RewriteCond %{HTTP_HOST} ^([a-z0-9-]+\.)?yourOLDdomain\.TLD$
RewriteRule (.*) http://yourNEWdomain.TLD/$1 [R=301]

It will also help the search engine to update their URLs for your blog entries as well as help you in technorati.

R=301 is HTTP 301 Permanent Redirect, which tells intelligent bots to adopt your new URL.

So anything http://yourOLDdomain.TLD/index.php/2888/12/25/TITLE will automatically be redirected to http://yourNEWdomain.TLD/index.php/2888/12/25/TITLE

If its in a subfolder just add the subfolder and it will work fine, like so:

RewriteCond %{HTTP_HOST} ^([a-z0-9-]+\.)?yourdomain\.TLD/subfolder$
RewriteRule (.*) http://yourNEWdomain.TLD/$1 [R=301]

Hope that helps.