Entanglement is one of the most striking features of quantum mechanics and it gives rise to situations that are not possible classically. For example, a subsystem can have more disorder than the whole system. Entanglement gives rise to some special applications such as quantum teleportation and superdense coding. This project is a study of entanglement. We define quantum entanglement and then study how to distinguish entangled and non-entangled (separable) states. To accomplish the latter goal, we study the concept of entanglement witness and the positive partial transpose (PPT) criterion. Then we study the disorder in composite systems when they are en- tangled and unentangled. In the end, we briefly look at some measures of entanglement such as the relative entropy of entanglement.