Analytical sociology is a theoretical and methodological approach within sociology that emphasizes the use of formal models, mathematical techniques, and computational methods to analyze social phenomena. It aims to uncover the underlying mechanisms and processes that generate patterns of social behavior and interaction.

Key aspects of analytical sociology include:

1. Formal Modeling: Analytical sociology employs formal models—mathematical representations of social processes and mechanisms—to study social phenomena. These models are often based on principles from game theory, network theory, and rational choice theory, and they provide a structured framework for analyzing social interactions, cooperation, competition, and decision-making.
2. Micro-Macro Linkages: Analytical sociology seeks to bridge the gap between micro-level individual behavior and macro-level social structures and patterns. It explores how individual actions and interactions aggregate to produce emergent social phenomena, such as social networks, norms, institutions, and collective behavior.
3. Mechanistic Explanations: Analytical sociology emphasizes mechanistic explanations of social phenomena, focusing on the underlying causal mechanisms and processes that generate observed patterns of behavior and outcomes. It aims to identify the specific mechanisms through which social phenomena emerge and evolve over time, often using simulation and computational modeling techniques to test and refine theoretical hypotheses.
4. Computational Methods: Analytical sociology utilizes computational methods, such as agent-based modeling, network analysis, and simulation, to study complex social systems and dynamics. These methods allow researchers to simulate the behavior of individual agents within a social context, explore the effects of different parameters and conditions on social outcomes, and generate new insights into the mechanisms driving social phenomena.
5. Interdisciplinary Approach: Analytical sociology adopts an interdisciplinary approach, drawing on insights and techniques from mathematics, computer science, economics, psychology, and other disciplines. It fosters collaboration and dialogue among scholars with diverse expertise to address complex social questions and challenges from multiple perspectives.
6. Empirical Applications: Analytical sociology applies formal models and computational methods to analyze a wide range of social phenomena, including social networks, group dynamics, cooperation, conflict, diffusion of innovations, and social change. It combines theoretical insights with empirical data analysis to develop testable hypotheses and refine theoretical frameworks.

Overall, analytical sociology offers a systematic and rigorous approach to studying social phenomena, focusing on uncovering the underlying mechanisms and processes that shape human behavior and social interactions. It complements traditional qualitative and quantitative methods in sociology and contributes to the advancement of knowledge about the dynamics of social life.