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We give a discussion of the classical Bowen$\unicode{x2013}$Series codingand, in particular, its application to the study of zeta functions and theirzeros. In the case of compact surfaces of constant negative curvature $-1$ theanalytic extension of the Selberg zeta function to the entire complex plane isclassical, and can be achieved using the Selberg trace formula. However, analternative dynamical approach is to use the Bowen$\unicode{x2013}$Seriescoding on the boundary at infinity to obtain a piecewise analytic expanding mapfrom which the extension of the zeta function can be obtained using propertiesof the associated transfer operator. This latter method has the advantage thatit also applies in the case of infinite area surfaces provided they do not havecusps. For such examples the location of the zeros is somewhat more mysterious.However, in particularly simple examples there is a striking structure to thezeros when we take appropriate limits. We will try to give some insight intothis phenomenon.  The survey is based on lectures given by the first author during the Workshopon Statistical Properties of Nonequilibrium Dynamical Systems which took placein July 2016 at South University of Science and Technology of China inShenZhen.

The Bowen$\unicode{x2013}$Series coding and zeros of zeta functions