**abstract:**
We will describe some methods, results and open problems of Real Algebra in the ring of analytic functions of an Analytic Manifold and the constructible sets defined by them, i.e. Semianalytic Geometry. In particular the following questions will be considered: description of the orderings of the meromorphic functions, Hilbert 17th Problem, Artin-Lang property, Null- and Positivstellensatz, connected components, separation, etc...

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