  We present a conceptually clear introduction to quantum theory at a level
suitable for exceptional high-school students. It is entirely self-contained
and no university-level background knowledge is required. The lectures were
given over four days, four hours each day, as part of the International Summer
School for Young Physicists (ISSYP) at Perimeter Institute, Waterloo, Ontario,
Canada. On the first day the students were given all the relevant mathematical
background from linear algebra and probability theory. On the second day, we
used the acquired mathematical tools to define the full quantum theory in the
case of a finite Hilbert space and discuss some consequences such as
entanglement, Bell's theorem and the uncertainty principle. Finally, on days
three and four we presented an overview of advanced topics related to
infinite-dimensional Hilbert spaces, including canonical and path integral
quantization, the quantum harmonic oscillator, quantum field theory, the
Standard Model, and quantum gravity.
