  The detection and classification of entanglement properties in a two-qubit
and a multi-qubit system is a topic of great interest. This topic has been
extensively studied, and as a result, we discovered various approaches for
detecting and classifying multi-qubit, in particular three-qubit entangled
states. The emphasis of this work is on a formalism of methods for the
detection and classification of bipartite as well as multipartite quantum
systems. We have used the method of structural physical approximation of
partially transposed matrix (SPA-PT) for the detection of entangled states in
arbitrary dimensional bipartite quantum systems. Also, we have proposed
criteria for the classification of all possible stochastic local operations and
classical communication (SLOCC) inequivalent classes of a pure and mixed
three-qubit state using the SPA-PT map. To quantify entanglement, we have
defined a new measure of entanglement based on the method of SPA-PT, which we
named as "structured negativity". We have shown that this measure can be used
to quantify entanglement for negative partial transposed entangled states
(NPTES). Since the methods for detection, classification and quantification of
entanglement, defined in this thesis are based on SPA-PT, they may be realized
in an experiment.
