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

Detection and Quantification of Entanglement in Multipartite Quantum Systems Using Weighted Graph and Bloch Representation of States