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The book Algorithm Design and Complexity: A Theoretical and Practical Approach offers a comprehensive exploration of the fundamental principles and advanced techniques involved in constructing and analyzing efficient algorithms. Combining theoretical rigor and practical application, the book covers classic design strategies such as divide and conquer, dynamic programming, greedy algorithms, backtracking and probabilistic algorithms, as well as discussing computational limits, complexity classes and intractable problems.Aimed at students, teachers and professionals in the field of computer science, the book presents content structured in a didactic way, accompanied by examples, pseudocode and exercises that promote the development of algorithmic reasoning. The analysis of time and space complexity is dealt with in depth, enabling the reader to evaluate the efficiency and scalability of their solutions.By integrating theory and practice, this book establishes itself as an essentialguide for anyone seeking to understand the fundamentals that underpin computational performance and to design robust, optimized algorithms that are applicable to the most diverse contexts of contemporary computing.