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The fundamental performance metrics of an intelligent reflective surface (IRS)-aided wireless system are presented. By optimizing the IRS phase-shift matrix, the received signal-to-noise ratio (SNR) is maximized at the destination in the presence of both reflected and direct channels. The probability distributions of this maximum SNR are tightly approximated for the moderate-to-large reflective element regime. Thereby, the probability density function and cumulative distribution function of this tight SNR approximation are derived in closed-form for Nakagami-m fading to facilitate a statistical characterization of the performance metrics. The outage probability, average symbol error probability, and achievable rate bounds are derived. By virtue of an asymptotic analysis in the high SNR regime, the diversity order is quantified. Thereby, we reveal that the overall diversity order can be scaled as a function of the number of reflective elements (N) such that Gd = mv + min(mg;mh)N, where mv, mh and mg are the Nakagami-m parameters of the direct, source-to-IRS and IRS-to-destination channels, respectively. The asymptotic achievable rate is derived, and thereby, it is shown that the transmit power can be scaled inversely proportional to N2. The impact of quantized IRS phase-shifts is investigated by deriving the achievable rate bounds. Useful insights are obtained by analyzing the system performance for different severity of fading cases including spatially correlated fading. Our analysis and numerical results reveal that IRS is a promising technology for boosting the performance of wireless communications by intelligently controlling the propagation channels without employing additional active radio-frequency chains.