Well, actually it is mariadb, but to start its client, I need to enter "mysql" in command line.
Anyway, after entering
mysql --user=root
Note, that at this time "root" doesn't have a password, so I successfully login and then:
SET PASSWORD FOR 'root'@'localhost' = PASSWORD('my_pass');
And it works, from now on I have to use "my_pass" to login.
But then I do:
sudo service mysql restart
And from now on, root's password is again reseted to "no password at all".
And again, to login I can't give any password.
Googling this doesn't help, because most articles are about "how to reset user password" :)
flush privilegesand now I have error: "Incorrect information in file: './mysql/tables_priv.frm' "