We build a mathematical theory of level sets of ''smooth'' real functions and surfaces. Similar results were obtained in the 1970s in Gamma-lines theory for an important but particular class of harmonic functions. In turn, Gamma-lines theory is similar to Nevanlinna theory of value distribution of meromorphic functions. Studies have progressed as follows. The classical Nevanlinna deficiency relation was transferred into Gamma-lines theory and in this paper we establish an analogous assertion for real functions and surfaces. It is therefore becoming apparent that Nevanlinna type phenomena have rather universal character in mathematics since the phenomena now have corresponding varieties in complex analysis, in real analysis and in geometry. Since the level sets admit interpretations in many applied sciences, one can hope that the new theory will be useful in applications. Note that in physics, for instance, the level set can be an isoterm, isobar, potential line, streaming line, or a set where chemical, oil, or radiation pollution have the same constant value.