Quantum theory is not an easy subject to master. Trained in the everyday world of macroscopic objects like locomotives, elephants and watermelons, we are insensitive to the beauty of the quantum world. Many quantum phenomena are revealed only in carefully planned experiments in a sophisticated laboratory. Some features of quantum theory may seem contradictory and inconceivable in the framework set by our experience. Rescue comes from the language of mathematics. Its mighty power extends the limits of our apprehension and gives us tools to reason systematically even if our practical knowledge fails. Mastering the relevant mathematical language helps us to avoid unnecessary quantum controversies.

Quantum theory, as we understand it in this book, is a general framework. It is not so much about what is out there, but, rather, determines constraints on what is possible and what is impossible. This type of constraint is familiar from the theory of relativity and from thermodynamics. We will see that quantum theory is also a framework, and one of great interest, where these kinds of question can be studied.

What are the main lessons that quantum theory has taught us? The answer, of course, depends on who you ask. Two general themes in this book reflect our answer: uncertainty and entanglement.

Uncertainty. Quantum theory is a statistical theory and there seems to be no way to escape its probabilistic nature. The intrinsic randomness of quantum events is the seed of this uncertainty. There are various different ways in which it is manifested in quantum theory.