Divided into three parts, this text includes results, reviews, and developments of some special topics on hydrodynamics, dynamical systems, astrophysics, quantum mechanics, relativity, and DNA evolution. The first part deals with hydrodynamics including historical aspects, applications of recent theories to extend the Navier-Stokes regime, and new results on known methods for going beyond the Navier-Stokes equations. The second part is devoted to dynamical systems including results on the problem of regularization of collisions and the Poincare continuation method. The second part also contains reviews of several aspects of the theory of dynamical systems. The third part deals with microquasars and astrophysics, fundamental aspects of quantum mechanics, superluminal propagation and DNA evolution.