I've never read any other book by John Gribbin, but I enjoyed
Schroedinger's Kittens. He wrote it as a kinf of sequel to
In Search of Schroedinger's Cat, so it assumes a bit mroe knowledge and the general introduction to quantum mechanics is fairly brief, if I remember right. It spends more time talking about the philosophical implications of quantum theory - what is the actual physical reality that our maths describes?; is that knowable or important?; that sort of thing.
I think the question the book tries to address can probably best be summed up thusly:
"Okay, so I know that it can behave like both a wave and a particle, but what actually
is it, really?"