Permissions set what a file's owner, group and others may each do, and you change them with chmod. Each class gets its own read, write and execute rights. In symbolic mode, u, g and o name the classes, so chmod u+x adds execute for the owner.
Each right has a number. Read is 4, write is 2 and execute is 1, and a class's digit is their sum. So 755 gives the owner every right and the rest read and execute.
ls -l shows the bits as letters. Here rwxr-xr-- gives the owner every right, lets the group read and execute, and lets others only read.
chown changes the owner and chgrp changes the group.
New files start from a default mode, 666 for files, and the umask removes bits from it, so the usual 022 gives 644.
# Change permissions using chmod
chmod 755 file.txt # rwxr-xr-x
chmod u+x script.sh # Add execute for owner
chmod g-w file.txt # Remove write for group
chmod o=r file.txt # Set others to read only
# Change ownership
chown user:group file.txt
chgrp newgroup file.txt
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