part I From Linear Algebra to Quantum Computing -- chapter 1 Basics of Vectors and Matrices -- chapter 2 Framework of Quantum Mechanics -- chapter 3 Qubits and Quantum Key Distribution -- chapter 4 Quantum Gates, Quantum Circuit and Quantum Computa- tion -- chapter 5 Simple Quantum Algorithms -- chapter 6 Quantum Integral Transforms -- chapter 7 Grover's Search Algorithm -- chapter 8 Shor's Factorization Algorithm -- chapter 9 Decoherence -- chapter 10 Quantum Error Correcting Codes -- part II Physical Realizations of Quantum Computing -- chapter 11 DiVincenzo Criteria -- chapter 12 NMR Quantum Computer -- chapter 13 Trapped Ions -- chapter 14 Quantum Computing with Neutral Atoms -- chapter 15 Josephson Junction Qubits -- chapter 16 Quantum Computing with Quantum Dots -- chapter A Solutions to Selected Exercises.