Abstract: Kodaira’s Embedding Theorem characterises compact complex manifolds that can be embedded in a projective space as those admitting a positive line bundle on it. Combining it with Chow’s Theorem, asserting that every complex projective variety is algebraic, it allows us to reduce problems of analysis to ones of algebra. After reviewing a few needed tools, such as linear systems and maps to projective spaces and blow-ups, I will present the classical proof of the result, relying on Kodaira’s Vanishing Theorem.