Tennis is a challenging sport that requires a comprehensive set of skills, including physical abilities, technical proficiency, and mental resilience. More importantly, tennis is also a game of strategy, demanding players to constantly evaluate the situation, calculate the shot placement and tactics, and control the flow of match. Chess, another game of strategy, has long benefited from the standard notation system, which enables deep and systematic analysis of game strategy in chess and even AI integration. In contrast, tennis currently lacks a structured and standardized framework for analyzing strategic game play. To bridge this gap, this paper presents Tennis Algebraic Notation System (TANS), a novel tennis notation system inspired by traditional chess notations. Unlike existing notation methods, TANS makes it easy for automated data extraction and analysis of game strategy and winning patterns. Using charted data with the new notation system, we can carry out analysis of match statistics and winning strategy analysis of tennis doubles matches. By summarizing tennis matches in a concise and information-rich notation system, we believe that TANS represents an important step toward enabling future systematic analysis of tennis strategy and AI-based game simulation.