  There has been spectacular progress in the field of quantum information in
recent decades. The development of this field highlights the importance of the
role of entanglement in quantum computing, quantum teleportation and quantum
cryptography. These notes serve to provide a gentle introduction to the
entanglement of bipartite states. In these notes, we introduce Bell's theorem
in the form derived by Clauser, Horne, Shimony and Holt. We discuss the Schmidt
decomposition and the Peres-Horodecki criterion in the entanglement of pure and
mixed bipartite states. Finally, we describe a teleportation protocol as an
illustration of the use of entangled states.
