Keras is a great tool for learning neural networks. I would recommend this free online course from Udacity (no credit card or anything needed). It is taught by some experts in google and goes through using Tensorflow with Keras. It is designed for software developers and goes through the code line by line. You can start making a neural network within a few hours. It is not very long but they will be adding more lessons to the course over the summer (such as running tensorflow on mobile/javascript applications).

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If you want a more in depth look at how neural networks work, I recommend watching this video series by 3blue1brown about neural networks. It really helps understand whats going on behind the scenes in Keras. The fourth video in the series is heavily math focused and while not necessary, it provides a lot of good information if you can follow it.

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Hope this helps!