The chapter introduces the concept of multicriteria optimization and decision making, emphasizing its relevance in real-world problems where multiple conflicting criteria must be balanced. It begins by defining multicriteria optimization as a task in system design and analysis, highlighting the importance of understanding the system's behavior and constraints. The chapter then delves into formal problem definitions, distinguishing between continuous and combinatorial optimization problems, and discussing the difficulty of these problems based on various factors such as multimodality, discontinuities, and the curse of dimensionality. The concept of Pareto dominance is introduced, explaining how it is used to compare solutions in multi-objective optimization. Pareto dominance is defined formally, and the chapter explores the properties of Pareto optimal solutions and the Pareto front. The chapter also covers the theoretical foundations of multi-objective optimization, including order theory, analytical methods, interactive methods, and meta-heuristic solution methods. It emphasizes the importance of understanding the mathematical modeling and foundations rather than focusing solely on specific algorithms. Finally, the chapter provides an overview of decision aid tools and formal methods for reasoning about conflicts, and it includes illustrative examples and case studies from various application domains such as economy, engineering, medicine, and social science. The aim is to provide a broad introduction to the field, making it accessible to MSc students without a strong background in mathematics by introducing basic numerical analysis concepts and providing numerical examples.The chapter introduces the concept of multicriteria optimization and decision making, emphasizing its relevance in real-world problems where multiple conflicting criteria must be balanced. It begins by defining multicriteria optimization as a task in system design and analysis, highlighting the importance of understanding the system's behavior and constraints. The chapter then delves into formal problem definitions, distinguishing between continuous and combinatorial optimization problems, and discussing the difficulty of these problems based on various factors such as multimodality, discontinuities, and the curse of dimensionality. The concept of Pareto dominance is introduced, explaining how it is used to compare solutions in multi-objective optimization. Pareto dominance is defined formally, and the chapter explores the properties of Pareto optimal solutions and the Pareto front. The chapter also covers the theoretical foundations of multi-objective optimization, including order theory, analytical methods, interactive methods, and meta-heuristic solution methods. It emphasizes the importance of understanding the mathematical modeling and foundations rather than focusing solely on specific algorithms. Finally, the chapter provides an overview of decision aid tools and formal methods for reasoning about conflicts, and it includes illustrative examples and case studies from various application domains such as economy, engineering, medicine, and social science. The aim is to provide a broad introduction to the field, making it accessible to MSc students without a strong background in mathematics by introducing basic numerical analysis concepts and providing numerical examples.