This volume 7 of the "Collected Works" includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1996 to 1999. At that time Arnold was focusing on the description of various spaces of curves, higher-dimensional continued fractions, pseudoperiodic topology, and unifying ideas related to symplectization, complexification and mathematical trinities in topology and mathematics in general...