Somewhat old, but might be helpful in getting some of the basic concepts clear, if you find Nielsen's "Neural Networks and Deep Learning" too difficult to start with.
Kevin Gurney “An introduction to neural networks” UCL Press, London, 1997
Makes a lot of the connection between biological neurons and artificial ones, which may or may not be helpful for your understanding. Please let me know if this books is useful for you.
Concentrate on chapters 3, 4 and 5.
