I've just finished this wonderful book. It explains how the Universe probably exists in more than the 4 dimensions that we can easily sense. Some theories work best in an 11-dimensional universe. Lisa Randall's own theory is roughly of a 4-dimensional brane that is somehow surrounded by a fifth dimension in which gravity can operate. She develops the history if the ideas from Newton onwards. The use of stories and allegories helps. Or you could catch some of the Youtube programmes she has done:
https://www.youtube.com/watch?v=TuL7gSMzLlU or
https://www.youtube.com/watch?v=SojWeJtYSr0&spfreload=5
