when you change the code to print out the values of $name, $1, and $2:

foreach $name (keys %book) {   #write the data
    print "$name \n";
    $name =~ /(.+)&(.+)/;
    print "$1, $2 \n";
    if ($2 =~ /^0$/) {
        print BOOK "$1,::";
    } else {
        print BOOK"$1,$2::";
    }
    for ( 0 .. $#{ $book{$name} } ) {
         print BOOK $def[$_+2] . ":" . $book{$name}[$_] . "::" unless 
+$book{$name}[$_] =~ /^0$/;
    }
    print BOOK "\n";
}
[download]

you get the correct output, and it shows $1 and $2 are initialized, but you still get the uninitialized error. Here is the output when you pass it School&0 and one number:

school&0

school, 0 
# Use of uninitialized value, <> chunk 7.
File 'untitled:Desktop Folder:Will's Stuff:Applications:MacPerl ƒ:phonebook'; Line 57

so that isnt the problem. Loop lables are a good idea, though, thanks