The Neuroscience book by Mark Bear gives a nice introductory overview of the biology behind a lot of neural processes:
If you're interested in computational neural models, I would highly recommend Wolfgram Gerstner's recent book (available for free online): http://neuronaldynamics.epfl.ch
The book by Dayan and Abbot on theoretical neuroscience is quite nice too: https://mitpress.mit.edu/books/theoretical-neuroscience
After this, you'll probably want to read new review papers, since it's a field that's moving quite fast now. (Especially with new measurement techniques in the past few years)
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