Abstarct: Entanglement is a kind of super strong quantum correlations which has long been recognized as an informational resource for quantum computations. The crucial role of the entanglement in trapped ionic and atomic systems, in photonic systems is obvious. It is believed that the entanglement, as conductivity in Mott insulator transition, quantum Hall effect and field induced magnetization, plays a substantial role in the understanding of quantum phase transitions. Recently, L. Amico, et al have studied a class of one-dimensional magnetic systems and found that entanglement shows scaling behavior in the vicinity of the transition point. T. Roscilde, et al have studied the quantum spin systems through entanglement estimators, the unusual order parameters. For the anisotropic spin-1/2 antiferromagnetic chain the entanglement estimators show abrupt changes at and around criticality, vanishing at the factorizing point, and then immediately recovering a finite value upon passing through the quantum phase transition. Measuring the entanglement of two particles is often an important task. Many efforts have been devoted to develop a quantitative theory of entanglement, including entanglement of formation, which is regarded as its basic measure. In this thesis we present the negativity in terms of correlation functions. The correlation functions show the collective critical behaviors of particles, as well as their ordering fluctuations in a system. We focus on the general class of parity-invariant quantum s=1, s=1/2 ferrimagnets and s=1 Heisenberg antiferromagnets. The negativity, a computable measure of the bipartite entanglement for the mixed states, is computed for these two different classes of magnets. The mixed spin heterogeneous ferrimagnets and spin-1 homogeneous magnets are the large class of quantum spin systems which have attracted much theoretical and experimental attention during last decade. By making use of the obtained form for the negativity we have also obtained the negativity of systems with different symmetries such as U(1), Z2, reflection and inversion or spin-flip symmetries.