I can suggest many things, but you need to specify exactly what you want to learn about.

There is a real distinction between "neuroscience" and "neurology". Neurology is clinical, and deals with stuff like stroke, epilepsy, and neurodegenerative disorders (Parkinson's etc.), as well as with the things more interesting to the layman, such as the stuff Oliver Sacks writes neat stories about. Neuroscience is more theoretical, and deals with anything from membrane biophysics and ion channels, to the function of single cells, to the broader functions of networks of neurons, computer simulations of neural networks, and brain/behavior studies.

If you really want to understand the stuff, the best textbook is Principles of Neural Science, by Kandel, Schwartz, and Jessel. It's definitely readable material for non-specialists, but you should read a little something on cell biology first, just so you know the basics of how cells (cells in general, including neurons) store information, produce the machinery that makes them run, make energy, etc.

G