About some directions of development permutations doctrine from the beginning of XIX century

Main directions of formation permutations doctrine from the beginning of XIX century were examined. Historical process of accumulation scientific results was described. Scientific contribution in structure and development doctrine XIX-XX centuries was indicated: G.A. Rothe, E. Bezout, P.S. de Laplace, M. Stern, O. Terquem, D. Andre, P. Spraque, J. Riordan, J. Touchard, A. Cayley, Jh. Muir, P. Tait and ets. Structure permutations doctrine to the middle of XX century was determined.