Psychology became a science of its own in the late 19th Century, and one of the best systematic introductions to it is still William James's "Psychology". One of its basic problems as a science is that its subject is given by a theoretical term: No person has the experiences of another person; all human experience is personal, private, and inaccessible to others except by inference, sympathy, or imaginatively taking another's place.

There are many introductions to psychology, and a few good ones. I listed below some, but anyone seriously interested in psychology should read William James.