Professor emeritus Kazimierz Goebel obtained his PhD in mathematics in 1967 at Maria Curie-Sklodowska University in Poland. Since 1963, he has been employed by UMCS and has served two three-year terms (1993-1999) as Rector of the university. At the same time, he has served as the President of the Polish Mathematical Society. Professor Goebel is the author of five books and over 70 scientific papers. He is a specialist in nonlinear problems of functional analysis, in particular metric fixed point theory. He has supervised and promoted 15 PhD students and is the visiting professor at several universities in the USA, Italy, Japan, Spain, Australia, Thailand. Moreover, he is a frequent short-term visitor, invited speaker and member of committees to a number of conferences and seminars, workshops and schools all over the world.Professor Stanislaw Prus graduated from Maria Curie-Sklodowska University, Poland, in 1979. He then obtained a PhD in mathematics in 1984 from the Mathematical Institute of Polish Academy of Science, Warsaw. Since 1979, he has been employed at UMCS and is now the author of over 45 scientific papers. Professor Prus is a specialist in the geometry of Banach spaces and nonlinear problems of functional analysis, and in particular of metric fixed point theory. He is also a frequent invited speaker and a member of committees to a number of conferences and seminars world-wide.

• 1: Basics and prerequisites 2: Low dimensional spaces 3: Strict and uniform convexity 4: Smoothness and uniform smoothness 5: Uniform smoothness vs uniform convexity 6: Projections on balls and convex sets 7: More moduli and coefficients 8: Radius vs diameter 9: Three special topics 10: Measures of noncompactness and related properties 11: The case of Banach lattices

...this excellent text covers a variety of attractive and important topics which are presented with elegance and concision. It is a welcome addition to the geometry of Banach spaces literature and can be warmly recommended to all students and faculty with an interest in functional analysis and related areas.