To understand sudo and "."

I am reading MySQL's manuals.

They suggest me that the command

cd /usr/local/mysql
sudo ./bin/mysqld_safe          // it seems that sudo = . + master rights

is the same as

. /usr/local/mysql/bin/mysql    // only ., no master rights

Are the two commands same in action?

. /some/path

executes [ or includes - which is execution ] a shell script you pointed.

./some/path

[ notice lack of space after dot ] executes program/script using relative path [ from current directory, not from the top of filesystem ]

sudo executes given command with other [ usually root ] user's privileges.

there is difference between

cd /usr/local/mysql
./bin/mysqld_safe

and

/usr/local/mysql/bin/mysqld_safe

the difference is current working directory. for mysql probably that does not meter, but for other/badly written programs that use relative paths - it might meter.

No, those commands are completely different. You may have a typo in there -- the following two commands are equivalent:

cd /usr/local/mysql
sudo ./bin/mysqld_safe

And:

sudo /usr/local/mysql/bin/mysqld_safe

From Freshmeat:

Sudo (su "do") allows a system administrator to delegate authority to give certain users (or groups of users) the ability to run some (or all) commands as root or another user while providing an audit trail of the commands and their arguments.

I'm not sure that you are confused about this, but you might be based on the question.

If you're only confused about why

cd /usr/local/mysql
./bin/mysqld_safe

Is the same as

/usr/local/mysql/bin/mysqld_safe

This is because in UNIX, the . means the current directory. So in this way, you will not search your PATH variable for the nearest mysqld_safe and run it, you will specifically run the one at /usr/local/mysql/bin/.