Fundamental Concepts -- Introduction and overview -- Introduction to quantum mechanics -- Introduction to computer science -- Quantum Computation -- Quantum circuits -- The quantum Fourier transform and its applications -- Quantum search algorithms -- Quantum computers: physical realisation -- Quantum Information -- Quantum noise, open quantum systems, and quantum operations -- Distance measurement for quantum information -- Quantum error-correction -- Entropy and information -- Quantum information theory -- Notes on basic probability theory -- Group theory -- Approximating quantum gates: the Solovay-Kitaev theorem -- Number theory -- Public-key cryptography and the RSA cryptosystem -- Proof of Lieb's theorem.