In this chapter, we begin by examining unique continuation properties for operators with non-analytic coefficients. We define the weak and strong unique continuation properties for linear differential equations. The weak property implies that if a solution is zero in some subset of the domain, it must be zero in the entire domain. The strong property extends this by stating that if a solution decays rapidly near a point, it must be zero in the entire domain. The strong property implies the weak one. The main goal of this chapter is to lay the groundwork for Carleman estimates, a technique introduced by Carleman in the 1930s. These weighted integral estimates depend on a parameter and have become a powerful tool in studying unique continuation properties, particularly for equations with non-analytic coefficients. This chapter also includes simple examples of Carleman estimates, preparing the reader for more general theory in later chapters. We will briefly discuss operators with constant coefficients, which, while now primarily of historical and pedagogical interest, help clarify the concept of Carleman estimates. Finally, we will present a theorem by Hörmander on the necessary conditions for Carleman estimates to hold for a differential operator.