This tutorial is an exposition of a rapidly growing new alternative approach to building computational models of cognition based on quantum theory. The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist/neural network movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly and widely applied that we take them for granted. Quantum theory provides a different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic; quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability; quantum reasoning does not obey the principle of monotonic reasoning. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach.