Principles of Neural Science, Sixth Edition (Eric R. Kandel, James H. Schwartz etc.)

This is a really great course, taking you from a beginner in neuro-science, to a high level. It's probably worth having some background in biology, but the first few chapters do give a very brief review of some relevant topics, like genetic techniques. I haven't finished reading it yet, but I find myself picking it up all the time.