If you already have a programming background I still recommend the second edition of "Programming Perl" by Larry Wall.

It is out of print now (the 3rd edition unfortunately has become a monster) but you can surely find it in a library (or somewhere in the darker corners of the internet).

For me it is the best book on a programming language I have ever read (but of course that is a matter of taste).

After that a must-read is the "Perl Cookbook".