The Enriques-Kodaira classification is a fundamental result in algebraic geometry that provides a complete and exhaustive classification of compact complex surfaces. The classification is based on the Kodaira dimension, which is a numerical invariant that measures the "complexity" of a surface. In this talk, we will discuss the Enriques-Kodaira classification in detail. We will begin by introducing the Kodaira Embedding Theorem which gives criteria for compact complex manifolds to be embedded into projective space. Then we will be discussing the Kodaira dimension and explaining its significance. We will then present the classification theorem itself, and we will discuss the different types of surfaces that arise in the classification. In addition to the classification theorem, we will also discuss some of the applications of the theorem to solve many important problems in algebraic geometry.