We give a overview of scientific works by V.V. Lychagin. A special attention is given to his prominent results in geometrical theory of partial differential equation, including: geometric theory of Monge-Ampére equations (in collaboration with A. Kusher and V. Rubtsov), solution of several longstanding problems on planar webs posed by W. Blaschke (together with V. Goldberg and M. Akivis), new developments in the theory of differential invariants: proof of the classical Lie-Tresse theorem (with B. Kruglikov), description of rational differential invariants for geometric and algebraic structures (in collaboration with P. Bibikov and N. Konovenko), colored calculus and quantization in monoidal categories (joint with P. Jakobsen and H. Huru), construction of cohomological invariants for solutions to the Einstein equations (in collaboration with V. Yumaguzhin), and finally research in formal integrability of partial differential equations based on the construction of multi-brackets (with B. Kruglikov).