There are three type of groups who can access a file in linux.
User: who created the file
Group: Group to which user belongs
Others: Other users (not belonging to above 2 categories).
To add/ modify permissions use following format
chmod u=rwx,g=rw,o=rx abc.txt
or a simpler option
chmod 765 abc.txt
Both of the above means same.
How to interpret these numbers
hence Read+Write+Exceite=4+2+1=7 or Read+ execute=4+1=5 and so on.