This book is dedicated to Professor Jindřich Nečas on his 70th birthday, featuring contributions from 61 mathematicians across 11 countries. It covers a wide range of research areas related to Nečas' work, including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions to parabolic and elliptic problems, operator theory, and numerical methods. The editors acknowledge the support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian, and express gratitude to Dr. Oldřich Ulrych and Dr. Šárka Matušů-Nečasová for their contributions. The book highlights Nečas' significant contributions to the fields of partial differential equations, nonlinear functional analysis, and their applications in continuum mechanics and hydrodynamics. It also includes a detailed biography of Nečas, detailing his academic career, research achievements, and collaborations with numerous mathematicians worldwide. The contents section lists the specific contributions and topics covered in the book, reflecting the breadth and depth of Nečas' scientific legacy.This book is dedicated to Professor Jindřich Nečas on his 70th birthday, featuring contributions from 61 mathematicians across 11 countries. It covers a wide range of research areas related to Nečas' work, including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions to parabolic and elliptic problems, operator theory, and numerical methods. The editors acknowledge the support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian, and express gratitude to Dr. Oldřich Ulrych and Dr. Šárka Matušů-Nečasová for their contributions. The book highlights Nečas' significant contributions to the fields of partial differential equations, nonlinear functional analysis, and their applications in continuum mechanics and hydrodynamics. It also includes a detailed biography of Nečas, detailing his academic career, research achievements, and collaborations with numerous mathematicians worldwide. The contents section lists the specific contributions and topics covered in the book, reflecting the breadth and depth of Nečas' scientific legacy.