This book presents fundamental concepts and seminal results to the study of vortex filaments in equilibrium. It also presents new discoveries in quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. It fills a gap in the vortex statistics literature by simplifying the mathematical introduction to this complex topic, covering numerical methods, and exploring a wide range of applications with numerous examples. The authors have produced an introduction that is clear and easy to read, leading the reader step-by-step into this topical area. Alongside the theoretical concepts and mathematical formulations, interesting applications are discussed. This combination makes the text useful for students and researchers in mathematics and physics.

"This book is devoted to the study of vortex filaments in equilibrium, quasi-2D vortex structures with applications to geophysical fluid dynamics and magnetohydrodynamics in plasmas. ? The text is useful for both researchers and students." (Maria Christina Mariani, zbMATH 1327.82001, 2016)

"This is a short but excellent research monograph that would be useful for the advanced study of and future research on vortex dynamics and its modern applications. I strongly recommend it to anyone interested in analytical and computational research on vortex filaments as well as quantum vortices and their applications. It would be suitableas a resource book for graduate-level research seminars for advanced graduate students and research professionals." (L. Debnath, Mathematical Reviews, May, 2015)