Classic Shannon information theory provides the mathematical framework for understanding and quantifying information in communication systems. It forms the backbone of modern telecommunications, data compression, and error correction. Shannon’s key insights revolve around defining the limits of information transmission and developing methods for efficiently encoding, transmitting, and decoding data, even in the presence of noise. Semantic communication is still in its early stage of research, in which the unified mathematical theory and performance evaluation system with generalization value are crucial to the development of semantic communication. This chapter discusses the basic fundamental mathematical framework and theory of semantic communications and the role of the performance evaluation metrics in the design and implementation of semantic communication systems.