Quantum mechanics is one of the most successful theories ever developed in science. However, ever since it was initially developed, about one hundred years ago, its meaning is still the subject of intense debate. But despite its interpretationalproblems, recently researchers started successfully applying the apparatus of quantum mechanics to the social sciences, such as quantum cognition and quantum finances.

In this tutorial we will start the first day with a quick overview of the quantum mechanical formalism. Then, in the second day we will discuss what makes quantum mechanics "quantum," i.e. how it departs from classical physics, and we will show how it violates Kolmogorov's axioms of probability, bringing even deeper conceptual and philosophical issues than some of the problems raised by the founders of quantum mechanics. Finally, in the last section we will present quantum models of cognition and finances, show how they can better fit empirical data, and end with somediscussions of how to think of quantum cognition as a theory of limited irrationality.

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