"As Riemann, Riemann-Stieltjes, and Lebesgue Integrals" is a specialized book that addresses fundamental concepts of integration theory. It provides a comprehensive introduction to measure theory, which serves as the foundation for Lebesgue integration. The authors, Marta Cilene Gadotti and Leandro Nunes dos Santos, explain the properties of Lebesgue integration and introduce Riemann-Stieltjes integration. Furthermore, significant results regarding the convergence of Lebesgue integrals are presented, which are not applicable in Riemann integration. This book is aimed at students and professionals seeking a deeper understanding of integration theory and wishing to recognize the differences between various integration methods.