Here is a self-contained version. As pan64 noted, you need to get your lines of input from somewhere (this is why $_ is uninitialized). You should just be able to use while (<>) { to read in from your python.txt file.

use warnings;
use strict;

my $chap;
my $sect;
while (<DATA>) {
    if (/^(\d+)/) {
        $chap = $1;
        $sect = 0;
    }
    else {
        $sect++;
        s/^/$chap.$sect /;
    }
    print;
}

__DATA__
1. Operators
Performing simple arithmetic
Operating on bitwise values
Comparing values
Operating on Boolean values
Operating on parts of a container with the slice operator
Understanding operator precedence
2. Regular Expressions
Using the re module
Searching with regular expressions
[download]

See also: perlintro