This book focuses on the creative elements of algorithmic design by delving into the phases involved in algorithm creation. The conceptual underpinnings of this creative process are analogous to the invention and development of mathematical theorems that result in the induction of combinatorial algorithms. Numerous issue examples are included in the book. It is intended to enhance readers' problem-solving abilities by imparting a grasp of the fundamental ideas behind algorithmic design. This book summarizes the most widely used computer algorithms and provides a comprehensive overview of algorithms and data structures for searching, sorting, and graph processing. The algorithms presented in this book represent a body of knowledge that has developed over the previous five decades and has become critical not just for professional programmers and computer scientists, but also for all students interested in mathematics, data science, and engineering. The reader of this book is meant to get knowledge about known ways for successfully resolving difficulties. They will become acquainted with various cutting-edge data structures and novel methods for utilizing data structures to improve the efficacy of algorithms. Because the book is virtually self-contained, it may be used as a course book, reference book, or self-study resource.