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Complex analysis is a form of surrealism and is one of the greatest creations of the human mind (see Figure 1 for another form of surrealism). It is both of this world and also of a netherworld of infinite beauty. Some of the behavior to be found in complex analysis is truly extraordinary, such as that of an analytic function in the neighborhood of an essential singularity taking every complex value infinitely many times with one possible exception. Or a family of meromorphic functions is normal if it omits three distinct values. All this originates from the primitive first steps of letting z = x + iy and a few rules to deal with its arithmetic. But therein are contained the seeds of the infinite complexity of Julia sets, where such astonishing sets are even found lurking in the innocuous looking Newton’s method once a change to a complex variable is made. As well we have such profound results as the Riemann mapping theorem, the Euler product formula, the second fundamental theorem of Nevanlinna, or such deep open questions as the Riemann hypothesis. If the latter turns out to be true, then something equally profound can be said about the distribution of prime numbers.