This chapter introduces the notion of complex scattering of waves, emphasizes the generality of the ideas involved, and explains its relevance to the field of nuclear physics and microwave cavities. It then introduces the subject of coherent wave transport through mesoscopic systems, e.g., disordered conductors and chaotic cavities, with emphasis on the statistics of fluctuations observed in these systems. These fluctuations, among them the universal conductance fluctuation, arise ultimately from the complex wave interference. Various length- and time-scales defining the mesoscopic system are discussed. The idea of maximum entropy approach (MEA) is introduced as distinct from, but related to, the idea of random-matrix theory (RMT) pioneered by Wigner originally in the context of isolated resonances of complex nuclei. The contents of this chapter include complex atomic nuclei and chaotic microwave cavities; wave localization; statistical fluctuations; mesoscopic conductors: time- and length-scales, ballistic mesoscopic cavities, diffusive mesoscopic conductors, and statistical approach to mesoscopic fluctuations.
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