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Digital communication using multiple-input multiple-output (MIMO) wireless links has recently emerged as one of the most significant technical breakthroughs in modern communications. This work presents an overview of some important theoretical concepts of MIMO systems. After describing the basic ideas of MIMO transmissions, information theoretical concepts like the system capacity and the mutual information for finite symbol alphabets of some prominent MIMO space-time designs are investigated. An evaluation of the error performance of these designs then leads toa more complete understanding of MIMO system parameters. Finally, the derived system capacity and the error performance is related to the framework of the diversity-multiplexing tradeoff. Each chapteris rounded by a number of simulations to deepen the understanding of the derived theoretical concepts.