md5sum creates file hashes. The hash is solely based on the file contents (even if you change the file name, the hash remains the same).
$ md5sum README.md bb4955b6d0855ce20c30223273124dd7 README.md
To create a file containing hashes, do:
$ md5sum README.md > MD5SUM.txt
To verify if the file was not tampered:
$ md5sum -c MD5SUM.txt README.md: OK