This collection is dedicated to the 60th anniversary of the prominent Russian mathematician and mechanic Valery Vasilyevich Kozlov. It features his key works across various fields of dynamical systems, written over the years. The selection of articles serves as an introduction to different areas of mechanics and mathematical physics. This publication will be invaluable for students, graduate students, and researchers in related fields. A notable strength of the collection is its overview of open problems in mathematics and mechanics, the solutions to which can be based on the works presented here. Additionally, the collection includes translations of articles by V.V. Kozlov that have only been published in English-language journals, making them difficult to access for Russian readers.