1. Finite-dimensional classical models, states and measurements, representation by diagonal matrices.
2. Finite-dimensional Hilbert spaces, Dirac formalism. Orthonormal bases, trace, Hilbert-Schmidt inner product. Special operators, spectral decomposition, functional calculus.
3. Finite-dimensional operator algebraic models, states, measurements, Born rule. Quantum bit, Bloch ball.
4. Extremal states and measurements, quantum indeterminism.  
5. Noiseless information transmission, perfect state discrimination. Quantum key distribution.
6. Composite systems, tensor product of Hilbert spaces and observable algebras.
7. Marginal states, partial trace. Product, separable and entangled states. Schmidt decomposition. Purification of states. Maximally entangled states, Bell bases.
8. Mathematical description of time evolution. Completely positive maps and their representations, Choi criterion, Kraus decomposition, Stinespring dilation. Naimark dilation of POVMs. Description of closed and open quantum systems.
9. Cloning and broadcasting of quantum states, no cloning theorem. Superdense coding, quantum teleportation.
10. Classical, quantum, and no-signaling correlations, non-local games, CHSH game, pseudo-telepathy games.