This book contains four main chapters.In the first three chapters we have considered the mutual interaction between three coupled oscillators, while the last main chapter we have considered the problem of two coupled oscillators. In the second chapter we examined the case in which the system contains the rotating and the counter rotating terms. The wave function,the Wigner function, as well as the Greens function in addition to the squeezing phenomenon are presented.In the third chapter we introduced the transition amplitude, however, for a different form of the system where the time-dependent is involved. In chapter four the effect of the phases is considered where the correlation and cross correlation functions are presented, this in addition to the quasi-probability distribution functions. In the fifth chapter we considered the most general time-dependent two coupled oscillators under the action of a stochastic driving force. The solution of the equations of motion beside the wave function are obtained, however, under a certain integrability condition where the relation between this condition and the stochastic force is considered.

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