What is a good beginner's book to read to get a greater understanding of neuroscience?
You could try this one: 30-Second Brain: The 50 Most Mind-blowing Ideas in Neuroscience, Each Explained in Half a Minute. ISBN-10: 184831647X. I haven't read it myself but it covers a really wide spectrum: single neurons, neural networks, brain architecture, awareness, perception, disease, ageing, etc. 
Importantly it's written by really good scientists in who are all currently doing really interesting things.