The main aim of this book is to introduce the study of unique continuation properties and stability estimates for inverse problems in partial differential equations (PDEs). Each topic covered is chosen with inverse problems in mind, though we believe all of them should be included in the training of those pursuing PDEs, especially regarding unique continuation properties. While excellent review articles and books exist on the subject, there remains a lack of a truly introductory text that begins with foundational principles, suitable for graduate or advanced undergraduate students who have some familiarity with Lebesgue measure theory, basic functional analysis, and an introductory PDEs course.