I read a lot! I read text books cover to cover. 1000 page computer manuals before breakfast. I also write books - though not nearly as fast as I read them! And, I review a lot of books and products. I review them for others who are wondering what book is worth the time and money because I spend a lot on stuff and some of it is a great value, and some is not. I think you need to read 3 books on any particular subject - there are usually only 3 that are essential on any particular subject, the rest are redundant or, in some cases, wrong. That being said, I usually read all of the books on a subject, even if they are wrong, because no one else (that I trust) has published the list of the 3 essential ones yet. [And, as a side note, at this time, I am not a reseller of any books I review and don't make any money from the reviews - if I like the book, I say so.]
So, the first essential book for parrot training is: Clicker Training for Birds by Melinda Johnson
Melinda gives a very thorough, clear, and readable explanation of the science of clicker training up front. I have read several books and seen several vidoes that mention clicker training where the author has just a little piece of the puzzle - Melinda lays out the whole thing. Why is timing so critical? Why a clicker? Why not my voice? Why is timing so critical? (I repeated that one because it is so critical).
Once the basics and background are down, she goes on to training specific behaviors and tricks. The last section of the books is a problem solving section: what if my parrot...? How do I handle it? The answers are great and cover just about everything. It is a thin book, but complete.
Here is the real bonus to this book - Melinda monitors the BirdClick Yahoo group (http://groups.yahoo.com/group/Bird-Click/) and answers questions by email! Reading a book and then being able to contact and interact with the author is always a great experience. The (unexpected) responses to my questions by Melinda have been exceptionally clear, helpful, and kind.
Bottom line: read this book first!