This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations. It is dedicated to Djairo G. de Figueiredo on the occasion of his 70th birthday. The collection of 34 research and survey articles reflects the wide range of interests of Djairo de Figueiredo, including: - various types of nonlinear partial differential equations and systems, in particular equations of elliptic, parabolic, hyperbolic and mixed type;- equations of SchrAdinger, Maxwell, Navier-Stokes, Bernoulli-Euler, Seiberg-Witten, Caffarelli-Kohn-Nirenberg;- existence, uniqueness and multiplicity of solutions;- critical Sobolev growth and connected phenomena;- qualitative properties, regularity and shape of solutions;- inequalities, a-priori estimates and asymptotic behavior;- various applications to models such as asymptotic membranes, nonlinear plates and inhomogeneous fluids.The contributions of so many distinguished mathematicians to this volume document the importance and lasting influence of the mathematical research of Djairo de Figueiredo. The book thus is a source of new ideas and results and should appeal to graduate students and mathematicians interested in nonlinear problems.