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Following the model of:

Provide QUALITY books and their approximate skill level in your answer. Add a short blurb/description about each book that you have personally read/benefited from. Books that meet the criteria will be added to the official community wiki answer.

Preferably, only outstandingly good books on Python 2 should be included as Python 3 is the future.

A tag search for "Python" and "Books" returns no complete book list results as of writing this question.

See also the Python Official Documentation and, from the official wiki, Python Books.

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This answer is to provide a reference of QUALITY books and an approximate skill level. Feel free to debate quality, headings, etc in your anwers or in the comments.

Reference

  1. Python Essential Reference - David Beazley
  2. Python in a Nutshell - Alex Martelli
  3. Python Pocket Reference - Mark Lutz

Introductory

  1. Programming in Python 3: A Complete Introduction to the Python Language - Mark Summerfield
  2. Python Programming: An Introduction to Computer Science - John Kelle
  3. Head First Python - Paul Barry

Intermediate

  1. Programming Python - Mark Lutz
  2. Dive Into Python 3 - Mark Pilgrim

Specialized

  1. Python Algorithms: Mastering Basic Algorithms in the Python Language - Magnus Lie Hetland
  2. Porting to Python 3: An in-depth guide - Lennart Regebro
  3. Python for Unix and Linux System Administration - Noah Gift and Jeremy M. Jones
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One book the above forgot that's excellent is Think Python, available at http://thinkpython.com That's for an introductory to computer science with Python. Excellent book, especially since it's free.

Also check out the Python section here: List of freely available programming books

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Dive Into Python

Dive Into Python -- Intermediate

I've read a ton of other python books, and Dive into Python is certainly my favorite. Oh, by the way, it's free. If you already know a language like C/Java/Perl this is the quickest way to get cracking with python-- this book doesn't waste your time with stuff you already know.

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Introductory

Invent your own computer games with Python by Al Sweigart

Specialized

Machine Learning: An Algorithmic Perspective by Stephen Marsland