The Compactness Theorem is a fundamental result in mathematical logic, particularly in the field of model theory. It states that if every finite subset of a set of first-order sentences has a model, then the entire set also has a model. This means that if you can satisfy all the sentences in smaller groups, you can satisfy them all together. This theorem has important implications in various areas of mathematics and logic. For example, it helps in proving the consistency of certain theories and is used in the study of infinite structures. The Compactness Theorem illustrates how local properties can lead to global conclusions in logical systems.