The book collects the most significant contributions of the outstanding Czech mathematician JindÅich NeÄas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with NeÄas's brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. The first part is devoted to the linear theory of partial differential equations. Its topics include the variational approach to linear boundary value problems and the Rellich - NeÄas inequalities, together with their applications to boundary regularity. The second part is concerned with the regularity for nonlinear elliptic systems, which are related to Hilbert's 19th and 20th problems. The third part focuses on Nonlinear Functional Analysis and its applications to non-linear PDEs, while the last part deals with topics in the mathematical theory of various models in Continuum Mechanics, including elasticity and plasticity, the Navier-Stokes equations, transonic flows, and multipolar fluids. The editorial contributions were written by: I. BabuÅ¡ka, P. Ciarlet, P. Drábek, M. Feistauer, I. HlaváÄek, J. JaruÅ¡ek, O. John, J. Kristensen, A. Kufner, J. Málek, G. Mingione, Å . NeÄasová, M. Pokorný, P. Quittner, T. RoubíÄek, G. Seregin and J. Stará.