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This edition is an almost exact translation of the original Russian text. A few improvements have been made in the present ation. The list of references has been enlarged to include some papers published more recently, and the latter are marked with an asterisk. THE AUTHOR vii LIST OF SYMBOLS M = M(X,T,rr. ) 1,3. 3 A(X,T) 2·7. 3 M(R) 2·9. 4 2 C [(Y ,T ,p) ,G,h] 3·16. 6 P = P(X,T,rr. ) 3,16. 12 1'3. 3 C9v [(Y ,T ,p) ,G,h] Px 2·8. 9 E = E(X,T,rr. ) 1,4. 7 Q = Q(X,T,rr. ) 1,3. 3 3,12. 8 Ey Q": = Q":(X ,T, rr. ) = Q#(X,T,rr. ) Ext[(Y,T,p),G,h] 3,16. 4 Ext9v[(Y,T,p),G,h] 3,16. 12 2·8. 31 Q":(R) = Q#(R) 3·13. 5 3,12. 12 Gy 3,15. 4 Sx(A) 2,8. 18 G(X,Y) SeA) 2·8. 22 2 3,16. 8 H [cY,T,rr. ),G,h] HE, (X,T,rr. ) = (X,T) 3'12. 12 1'1. 1 Y (X,T,rr. ,G,a) 4·21. 4 3'16. 1 Hef) HK(f) 4·21. 9 H(X,T) 2,7. 3 1- 3,19. 1 L = L(X,T,rr. ) 1,3. 3 viii I NTRODUCTI ON 1. It is well known that an autonomous system of ordinary dif ferential equations satisfying conditions that ensure uniqueness and extendibility of solutions determines a flow, i. e. a one parameter transformation group. G. D.