I am new to Python and I'm interested in learning the basics. Can anyone recommend a good training course (online or otherwise) for a beginner with no programming experience?

I used Codecademy to teach myself. There's a free online course there which takes about twelve hours (or so) to go through. It was nice and easy and went through things in a good level of detail.

My recommendation is the PyCharm Educational Edition.

PyCharm is an integrated development environment used by some software developers at the CCDC. You can think of it as a Python-aware text editor with various useful features like one-click execution of your Python scripts. It is a free download, and that particular version comes with a built-in tutorial that teaches the most basic parts of the Python syntax.

It is used in schools, so is quite simple and intuitive.

Once you've been through that, I think that the best way to learn is to do! Just pick a simple task (make a list of all entries containing caffeine, say) and write a script to do it. If you get stuck, please don't hesitate in posting questions on this forum or on a Python-specific forum such as http://www.python-forum.org/

On Michael Kennedy's blog is a very useful Python Cheat Sheet for beginning to intermediate Python developers.

In the Django Girls Tutorial is a very good Introduction to Python for beginners without programming experience.  

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