He also has a fantastic article specifically about recurrent neural networks here: http://karpathy.github.io/2015/05/21/rnn-effectiveness/
In terms of learning, I would also encourage people to try the materials from our CS231n class - this is a class I taught at Stanford last quarter with my adviser. It's technically about Convolutional Networks, but most of the class material is building up generic Neural Networks, backprop, and so on. You can also try our IPython Notebook assignments.
Course notes: http://cs231n.github.io/ Syllabus with slides too: http://cs231n.stanford.edu/syllabus.html
Another good pointer is Andrew Ng's Coursera class - that's a thorough introduction as well.
I also recommend the tutorials on http://deeplearning.net/tutorial/ (Python / Theano)
And Andrej Karpathy's blog is also a great resource for explanations of deep learning concepts in simple terms: https://karpathy.github.io/
There is a book that I can link if you are interested.