Quantum theory is one of the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. This text introduces senior undergraduate and postgraduate students to the theory's fundamental conceptual and philosophical problems. Most students are taught about quantum theory as though these problems do not exist or are irrelevant to their understanding. Either by design or default they are fed the orthodox "Copenhagen interpretation", originally developed by Niels Bohr and his colleagues in the 1920s and 1930s. When faced with the theory's inherent non-understandability under this interpretation, students are likely to blame themselves for failing to come to terms with what is one of the most important and successful theoretical foundations of modern physical science. Most academic textbooks on the subject are written for specialists, filled with complex jargon and dense mathematics and are unsuitable for undergraduates.