Mathematical sociology, a field dedicated to applying mathematical techniques to the study of social phenomena, has evolved significantly over the past few decades. This chapter reviews the progress made in this interdisciplinary domain, focusing on key methodologies, recent advancements, and emerging trends. We explore the application of graph theory, game theory, agent-based models, and statistical methods in understanding social networks, collective behavior, and social dynamics. Additionally, we examine how big data and computational tools have transformed the field, and discuss future directions and challenges, including the need for greater model realism and ethical considerations. This chapter aims to provide a comprehensive overview of how mathematical methods have advanced sociological research and their implications for future studies.