  This thesis is an attempt to enhance understanding of the following questions
A- Given a multipartite quantum state (possibly mixed), how to find out whether
it is entangled or separable? (Detection of entanglement.) B- Given an
entangled state, how to decide how much entangled it is? (Measure of
entanglement.), in the context of multipartite quantum states.
  We have explored two approaches. In the first approach, we assign a weighted
graph with multipartite quantum state and address the question of separability
in terms of these graphs and various operations involving them. In the second
approach we use the so called Bloch representation of multipartite quantum
states to establish new criteria for detection of multipartite entangled
states. We further give a new measure for entanglement in $N$-qubit entangled
pure state and formally extend it to cover $N$-qubit mixed states.
