This chapter recalls fundamental concepts from real and functional analysis, such as smooth and Hölder spaces, measure theory, and \( L^p \) spaces, along with the partition of unity. Key theorems, including the extension theorem, the Lebesgue differentiation theorem, and the divergence theorem for Lipschitz domains, are also presented. The chapter introduces the Hausdorff distance and the distance function, which are crucial for studying inverse problems with unknown boundaries. These foundational results bridge basic analysis and research-level topics. Readers familiar with these concepts may skip this chapter and refer back as needed.