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The capacity of multiple-input multiple-output (MIMO) wireless communication systems over spatially correlated Rayleigh distributed flat fading channels with complex Gaussian additive noise is investigated. Specifically, the probability density function of the mutual information between transmitted and received complex signals of MIMO systems is derived. Using this density the closed-form ergodic capacity (mean), delay-limited capacity, capacity variance and outage capacity formulas for spatially correlated channels are derived and then these formulas are evaluated numerically. Numerical results show how the channel correlation degrades the capacity of MIMO communication systems. It is also shown that the density of mutual information of correlated/uncorrelated MIMO systems can be approximated by a Gaussian density with derived mean and variance, even for a finite number of inputs and outputs.