Notes on unique continuation properties for Partial Differential Equations -- Introduction to the stability estimates for inverse problems

These Notes are intended for graduate or undergraduate students who have familiarity with Lebesgue measure theory, partial differential equations, and functional analysis. The main topics covered in this work are the study of the Cauchy problem and unique continuation properties associated with partial differential equations. The primary objective is to familiarize students with stability estimates in inverse problems and quantitative estimates of unique continuation. The treatment is presented in a self-contained manner.