MYSQL_Backup.sh

#!/bin/sh
# init. the projects informations
PROJECT=PROJECT_NAME
FILE=$PROJECT.`jdate +%Y-%m-%d`.sql
DBSERVER=DATABASE_SERVER
DATABASE=DBNAME
USER=DBUSER
PASS=dbpassword

#in case you run this more than once a day, remove the previous version of the file
unalias rm     2> /dev/null
rm ${FILE}     2> /dev/null
rm ${FILE}.gz  2> /dev/null

#do the mysql database backup (dump)

# use this command for a database server on a separate host:
#mysqldump --opt --protocol=TCP --user=${USER} --password=${PASS} --host=${DBSERVER} ${DATABASE} > ${FILE}

# use this command for a database server on localhost. add other options if need be.
mysqldump --opt --user=${USER} --password=${PASS} ${DATABASE} > ${FILE}

#gzip the mysql database dump file
gzip $FILE

#show the user the result then move it to a destination then push it to it's git repo
echo "${FILE}.gz was created:"
ls -l ${FILE}.gz
mv ${FILE}.gz /root/backup/${PROJECT}/${DATABASE}/
git add ${FILE}.gz && git commit -m `jdate +%Y-%m-%d` && git push -u origin master

It could be GZipped in one line,
Besides, I think you should insure about the successful process of sqldump and gzip and then echo:

mysqldump --opt --user=${USER} --password=${PASS} ${DATABASE} | gzip > $FILE.gz && echo "${FILE}.gz was created:" && ls -l ${FILE}.gz

Also, I think it would be better to use Gregorian date.

@eXtrem0us i saw you comment after a year :)))
I think i was drunk when i wrote this script.
By the way thank you. i will change the script <3