This book offers a modern introduction to Nevanlinna theory & its intricate relation to the theory of normal families algebraic functions asymptotic series & algebraic differential equations Following a comprehensive treatment of Nevanlinna's theory of value distribution the author presents advances made since Hayman's work on the value distribution of differential polynomials & illustrates how value- & pair-sharing problems are linked to algebraic curves & Briot-Bouquet differential equations In addition to discussing classical applications of Nevanlinna theory the book outlines state-of-the-art research such as the effect of the Yosida & Zalcman-Pang method of re-scaling to algebraic differential equations & presents the Painleve-Yosida theorem which relates Painleve transcendents & solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions Aimed at graduate students interested in recent developments in the field & researchers working on related problems Nevanlinna Theory Normal Families & Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area With examples exercises & proofs seamlessly intertwined with the body of the text this book is particularly suitable for the more advanced reader