In the theoretical part of this bachelor thesis, the types of radioactivity, law of radioactivity as well as the meaning of radioactivity in general are described. The basic dosimetric quantities and its units are defined. After that, the physical and chemical properties of radon and its short-lived progeny are introduced. The sources of radon are specified and the mechanisms of entering the houses as well as the importance of protecting and decreasing radon levels in houses are emphasized. The impact of radon issue on public health and related experimental research are commented.The method of radon measurement by nuclear track etched detectors is described in experimental part of this thesis . The way of producing, setting up and collecting of detectors as well as the way of their analysis is briefly described. The obtained data are presented in tabular and graphical ways. Two indoor radon maps are produced: one using administrative borders of Međimurje county and the other using grid cell approach. Indoor radon concentrations were in range from 11 to 528 Bq m^{-3}. The averaged equilibrium factor was 0.55 . The population of the Međimurje county receive the annual effective dose equivalent due to radon and its short-lived progeny of 2.09 mSv in average.