The Springer Monographs in Mathematics series publishes advanced monographs that present the "state-of-the-art" in mathematical research fields that have reached a level of maturity suitable for such treatment. These books are self-contained and accessible to a broad audience, while also being comprehensive and valuable references for many years. They also highlight the relevance of the subject to neighboring areas of mathematics and suggest future research directions. The second edition of "Mittag-Leffler Functions, Related Topics and Applications" presents new ideas and results related to the theory and applications of Mittag-Leffler functions. New results have been added to practically all sections of the book. Chapter 3 discusses Mittag-Leffler summation and the Mittag-Leffler reproducing kernel Hilbert space. Chapter 4 discusses the two-parametric Mittag-Leffler function and its applications to inverse problems for differential equations in Banach spaces. Chapter 5 discusses three-parametric Mittag-Leffler functions, including recent results on Le Roy type functions. Chapter 6, which has been significantly enlarged, discusses Mittag-Leffler functions depending on several parameters, including their properties and numerical methods. The chapters on applications have been completely rewritten, including discussions on fractional order equations, deterministic models, and stochastic models. A new chapter on the classical Wright function is also included. The book is a collaboration between researchers in Berlin, Bologna, and Minsk. It has benefited from visits and exchanges between the authors. The authors express their gratitude to colleagues and friends for their support. The book is dedicated to the memory of Anatoly Kilbas and Rudolf Gorenflo, who were essential to the project's realization. The book covers the history, theory, and applications of Mittag-Leffler functions, including their relation to fractional calculus and their use in various scientific disciplines. It includes detailed discussions on the properties of Mittag-Leffler functions, their integral representations, asymptotics, and their applications in differential equations, stochastic models, and deterministic models. The book also includes a comprehensive list of references and an index.The Springer Monographs in Mathematics series publishes advanced monographs that present the "state-of-the-art" in mathematical research fields that have reached a level of maturity suitable for such treatment. These books are self-contained and accessible to a broad audience, while also being comprehensive and valuable references for many years. They also highlight the relevance of the subject to neighboring areas of mathematics and suggest future research directions. The second edition of "Mittag-Leffler Functions, Related Topics and Applications" presents new ideas and results related to the theory and applications of Mittag-Leffler functions. New results have been added to practically all sections of the book. Chapter 3 discusses Mittag-Leffler summation and the Mittag-Leffler reproducing kernel Hilbert space. Chapter 4 discusses the two-parametric Mittag-Leffler function and its applications to inverse problems for differential equations in Banach spaces. Chapter 5 discusses three-parametric Mittag-Leffler functions, including recent results on Le Roy type functions. Chapter 6, which has been significantly enlarged, discusses Mittag-Leffler functions depending on several parameters, including their properties and numerical methods. The chapters on applications have been completely rewritten, including discussions on fractional order equations, deterministic models, and stochastic models. A new chapter on the classical Wright function is also included. The book is a collaboration between researchers in Berlin, Bologna, and Minsk. It has benefited from visits and exchanges between the authors. The authors express their gratitude to colleagues and friends for their support. The book is dedicated to the memory of Anatoly Kilbas and Rudolf Gorenflo, who were essential to the project's realization. The book covers the history, theory, and applications of Mittag-Leffler functions, including their relation to fractional calculus and their use in various scientific disciplines. It includes detailed discussions on the properties of Mittag-Leffler functions, their integral representations, asymptotics, and their applications in differential equations, stochastic models, and deterministic models. The book also includes a comprehensive list of references and an index.