Susan Greenfield is a neuroscientist, so she knows her stuff when it comes to the brain. In this fascinating and accessible book, she explores the idea of identity. As you might expect, it's complex and not explained by any simple factor or mechanism within the brain, and in fact is not really fully understood. However she clearly describes three main types of identity, ranging from Someone, through Anybody to Nobody.
In brief, Someone is the sense of self as a unique individual, separate from everyone else. Anybody is being part of a group, where you can lose your sense of individuality and become part of a bigger group identity. Finally Nobody is where neither of these is experienced and in a sense your identity is simply a stream of physical sensations.
These three states are present to some extent in all of us - for example being taken up in the joint thrill of a football crowd (if that's your thing) is to be Anybody, or loosing yourself by becoming drunk (or on drugs) is to be Nobody.
The first part of the book is perhaps the most difficult because she lays down the basics of how the brain works: but it's a necessary foundation for what follows. Then towards the end she explores how the modern digital age might presage change - in fact she argues that the changes wrought could be so profound that a post-digital society might have a completely different way of identifying self as a result.
You may not agree with all her ideas, but they are certainly thought provoking and always clearly argued. It's about 4 years old now, but doesn't feel out of date. If anything the latter parts seem even more relevant now.