dStudying open quantum systems and solving the master equation for density matrix is the main part of modern quantum physics and it is very important in quantum optics, condensed matter physics and quantum computations. In this thesis, multi-qubit and multi-qutrit systems in dissipative environments have been studied. Then by considering effects of environment's noise, entanglement and quantum discord dynamics among qubits and qutrits have been investigated. Moreover, the possibility of generation of entanglement between two-qubit spin chain is considered. Our results show that for a multi-qubit system in dissipative environment, if we assume that initially only one of the qubits is in the excited state while all the others are in the ground state, after a period of time under the influence of the dissipative environment quantum correlation will generate between this qubit and the others. This result is true for a multi-qutrit system in dissipative environment,too. Also, for a two-spin chain in dissipative environment, if we assume that initially one of the spins is up and the other one is down, after a while entanglement will generate between two spins.Another result is that for a two-qubit system with initially Bell-state under the influence of amplitude damping and phase damping channel, entanglement will be reduce