The Physics of Star Trek was the first book on physics I had ever read, and it was the one of the things that really got me hooked on the subject. I cannot recommend enough. Do not worry if you cannot understand everything; I couldn't until I got a little deeper into the topics they present.
I would also suggest Physics of the Impossible by Michio Kaku for when you finish The Physics of Star Trek. It is a little harder, but it explores similar things like force fields and time travel. It is also a little more up to date. Kaku also divides the book into three parts: Class I Impossibilities, Class II Impossibilities, and Class III Impossibilities. They give a better idea of what may actually become a possibility. I would highly recommend both books. Enjoy reading.
I'll see if its in the library. :-) It sounds like something I'd like. I finished The Physics Of Star Trek (and somewhere within that time period I had turned into a total trekker), and found Beyond Star Trek by the same author. Its about Star Trek, X-files and Cloverfield, and I've only watched Star Trek, so I'll look into the other things before I read that.
I haven't read "The Physics of Star Trek", but I can back up that recommendation for "Physics of the Impossible". It did a good job at stimulating my imagination and inspiring me to stick with the engineering major. I still think about utilizing some of the technology mentioned in the book, along with similar technology. Kaku (the author) also talks a lot about Star Trek and other science fictions too in the book, such as the use of "force fields" and "phasers".