History of Science and Engineering Annotation << Back Euler’s Algorithm for Search of Hamiltonian Cycles and Paths Shukhman E.V. The article observes Euler’s algorithm for solution of the knight’s tour problem. Also we study the possibility of Euler’s algorithm modification to solve actual problems reduced to finding Hamiltonian cycles and paths. First we publish in Russian Euler’s notes from his notebooks, related to this problem. The experimental study of effectiveness of the Euler’s algorithm was performed. It is shown that the Euler’s algorithm gives significant performance benefits compared to backtracking algorithms. We research the general problem of finding a Hamiltonian cycles and paths as well as its practical application, and have performed the analysis of using Euler’s algorithms for its solution. Keywords: history of mathematics; knight’s tour problem; Leonhard Euler; Hamiltonian cycles and paths. Contacts: E-mail: shukhman.elena@gmail.com Pp. 03-11.