P.V. SUBRAHMANYAM is a Professor Emeritus at the Indian Institute of Technology Madras (IIT Madras), India. He received his PhD in Mathematics from IIT Madras, for his dissertation on "Topics in Fixed- Point Theory" under the supervision of(late)Dr. V. Subba Rao. He received his MSc degree in Mathematics from IIT Madras, and BSc degree in Mathematics from Madras University. He has held several important administrative positions, such as senior professor and head of the Department of Mathematics at IIT Madras; founder and head of the Department of Mathematics at the Indian Institute of Technology Hyderabad (IIT Hyderabad); Executive Chairman of the Association of Mathematics Teachers of India(AMTI); president of the Forum for Interdisciplinary Mathematics (FIM).Before joinining IIT Madras he served as a faculty member  at Loyola College, Madras University, and Hyderabad Central University. His areas of interest include classical analysis, nonlinear analysis and fixed-point theory, fuzzy- set theory, functional equations and mathematics education. He has published over 70 papers and served on the editorial board of the Journal of Analysis and the Journal of Differential Equations and Dynamical Systems. He received an award for his outstanding contributions to mathematical sciences in 2004 and the Lifetime Achievement Award from the FIM in 2016. He has given various invited talks at international conferences and completed brief visiting assignments in many countries such as Canada, Czech Republic, Germany, Greece, Japan, Slovak Republic and the USA. He is also a life member of the Association of Mathematics Teachers of India, FIM, Indian Mathematical Society and the  Society for Industrial and Applied Mathematics(SIAM).

Chapter 1. Prerequisites.- Chapter 2. Fixed Points of Some Real and Complex Functions.- Chapter 3. Fixed Points and Order.- Chapter 4. Partially Ordered Topological Spaces and Fixed Points.- Chapter 5. Contraction Principle.- Chapter 6. Applications of the Contraction Principle.- Chapter 7. Caristi's ¿xed point theorem.- Chapter 8. Contractive and Nonexpansive Mappings.- Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings.- Chapter 10. Brouwer's Fixed Point Theorem.- Chapter 11. Schauder's Fixed Point Theorem and Allied Theorems.- Chapter 12. Basic Analytic Degree Theory af a Mapping.