
Away from understanding the eavesdropping strategies there cannot be talking about a secure quantum key distribution. And also the one of key problem which is solved by using quantum techniques is that of eavesdropping detection. When bearing in mind about the Experimental Quantum Cryptography it has been tremendous improvement during the past few years. Experimental cryptography and the limitations of practical cryptography is also a major research area of Quantum Cryptography. However, there are some other cryptographic applications as well, such as bit commitment. When exploring about the Quantum Cryptography, in general the focus goes only into the key distribution. In particular, we review Quantum Key Distribution (QKD) using the BB84 protocol, B92 protocol and also with a short description about other existing protocols as well. After a brief introduction to Classical Cryptography systems, we provide the quantum mechanical background needed to present some fundamental protocols of Quantum Cryptography. This study was the result of a little effort to bring onward some interesting facts in Quantum Cryptography (QC). The recent application using the principles of Quantum Mechanics to cryptography has led to an unbelievable new dimension in secret communication. A table of contents as well as an index are provided for readers who wish to "pick and choose." Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication from the very elementary to the more advanced. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no-cloning theorem, quantum teleportation, Shor's algorithm, Grover's algorithm. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit.

The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory.
