I suspect the error you listed is occurring because there is a gap in the array that you created. As in this example:

use Data::Dumper;
my @array = ();
$array[0] = [1];
$array[2] = [2];
@array = sort { $$a[0] cmp $$b[0]} @array;
print Dumper \@array;
[download]

As for the sorting algorithm, the most common approach would be something like this:

use strict;
use warnings;
use Data::Dumper;

my @courselist = ( 
    ["UM", "CS 34", ],
    ["AC", "PHIL 13", ],
    ["UM", 'BIO 567', ],
    ["UA", 'BIO 999', ],
    ["UM", 'BIO 1', ],
);  


@courselist = sort {$$a[0] cmp $$b[0] or $$a[1] cmp $$b[1]} @courselis
+t;
print Dumper(\@courselist);
[download]

As for the problem you are solving, it would probably be faster and easier to handle the sorting in a database, where the book information should probably be stored. Good luck with the project, I'll stop by your store next time I'm in Amherst :)