This book discusses, in clear non technical language, the two major theories of twentieth-century physics: relativity and quantum mechanics. They are discussed conceptually and philosophically, rather than using mathematics, and the philosophical issues raised pertain to much of science, not only physics. The book is based on successful courses taught by the author, who shows how new discoveries forced physicists to accept often strange and unconventional notions. He aims to remove the mystery and misrepresentation that often surround the ideas of modern physics and to show how modern scientists construct theories. In this way, the reader can appreciate their successes and failures and understand problems which are as yet unsolved.