This chapter introduces general measures and outer measures, highlighting their interplay. It discusses how outer measures generate measures and how measures induce outer measures. The extension of measures to complete measures and outer measures to regular outer measure is discussed. The discussion covers Lebesgue-Stieltje’s outer measure and Hausdorff measure. The chapter also explores measurable functions, integration in product spaces, product measures, and the integration of complex-valued functions. Relevant theorems and exercises reinforce these concepts.