This book provides a comprehensive survey and investigation into the monotonicity conditions applied to the coefficients of trigonometric (or Fourier) series, exploring how these conditions influence various convergence properties, along with related topics on positivity and monotonicity. Highlighting recent breakthroughs, the book offers a systematic review of the history and development of this area, focusing on current ideas, methods, and techniques to equip readers for future advancements.Designed to be both systematic and original, the book serves as an accessible resource for mathematicians and students in analysis. With its self-contained approach, it requires only a basic knowledge of analysis, making it suitable as an advanced textbook for graduate students or a reference for researchers interested in this field.