This book will provide an overview of the current approaches for analyzing algorithm performance in different commonly used scenarios by emphasizing issues that are often overlooked. The book will also show how these issues can be easily avoided by applying principles that lead to Deep Statistical Comparison and its variants. The focus will be on statistical analyses performed using single-objective and multiobjective optimization data. At the end of the book, examples of a recently developed web-service-based e-learning tool, known as DSCTool, will be presented. The tool provides the users with all the required functionalities in order to make a proper robust statistical comparison analysis in different statistical scenarios.The authors have presented the related tutorial at the significant related international conferences in Evolutionary Computing, including GECCO, PPSN, and SSCI, and the book is approved for publication in our Natural Computing book series.