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This book focus on the theory and practice of discrete optimization. The book contains an explanation of many different continuous and discrete algorithms designed for optimizing different problems and applications. The subjects addressed in this book are important for both mathematics and computer science researchers. I hope that the readers of this book will find many fruitful ideas for their own future research in the field of discrete optimization.Discrete optimization is an important area of applied mathematics that is at the intersection of several disciplines and covers both theoretical and practical aspects. I present new theoretical results, structural investigations, new models, and algorithmic approaches, as well as new applications of discrete optimization problems. Among the possible subjects, integer programming, combinatorial optimization, optimization problems on graphs and networks, scheduling, and logistics are mentioned, to name a few. This book is of high quality, reflecting the great interest in the area of discrete optimization.