The chapter introduces the field of structural optimization, highlighting its rapid development and the growing importance of practical applications in various engineering fields such as automotive, aerospace, and civil engineering. The authors emphasize the challenge of developing optimization methods that are compatible with complex general-purpose software packages used by engineers for structural analysis. They introduce sequential approximate optimization techniques, which use the analysis package to construct an approximation of the design problem and then apply mathematical optimization techniques to solve it. The book is structured to cover the theoretical foundations of optimization, the construction of approximate problems, and the evaluation of results, with a focus on minimizing computational costs and maximizing efficiency. The content is suitable for graduate courses in structural optimization, depending on the students' prior knowledge in optimization techniques. The authors also acknowledge the contributions of several reviewers and the use of TeXtures software for typesetting.The chapter introduces the field of structural optimization, highlighting its rapid development and the growing importance of practical applications in various engineering fields such as automotive, aerospace, and civil engineering. The authors emphasize the challenge of developing optimization methods that are compatible with complex general-purpose software packages used by engineers for structural analysis. They introduce sequential approximate optimization techniques, which use the analysis package to construct an approximation of the design problem and then apply mathematical optimization techniques to solve it. The book is structured to cover the theoretical foundations of optimization, the construction of approximate problems, and the evaluation of results, with a focus on minimizing computational costs and maximizing efficiency. The content is suitable for graduate courses in structural optimization, depending on the students' prior knowledge in optimization techniques. The authors also acknowledge the contributions of several reviewers and the use of TeXtures software for typesetting.