Owing to the existence of a dilatation generator of eigenvalues ± 2 , ± 1 , 0 \pm 2, \pm 1,0 the symplectic Lie algebra is considered as a | 2 | |2| -graded Lie algebra. The corresponding decomposition of the symplectic group Sp(2( n + 1 ), R ) {\text {Sp(2(}}n + 1{\text {),}}{\mathbf {R}}{\text {)}} makes the semidirect product (denoted L 0 {L^0} ) of the ( 2 n + 1 ) (2n + 1) -dimensional Weyl group by the conformal symplectic group CSp( 2 n , R ) {\text {CSp(}}2n,{\mathbf {R}}{\text {)}} appear as a privileged subgroup and permits one to construct a 2 n + 1 2n + 1 -dimensional homogeneous space possessing a natural contact form. Then Sp ( 2 ( n + 1 ) , R ) {\text {Sp}}(2(n + 1),{\mathbf {R}}) -valued Cartan connections on a L 0 {L^0} principal fibre bundle over a 2 n + 1 2n + 1 -dimensional manifold B 2 n + 1 {B_{2n + 1}} are constructed and called symplectic Cartan connections. The conditions for obtaining a unique symplectic Cartan connection are given. The existence of this unique Cartan connection is used to define the notion of contact structure over B 2 n + 1 {B_{2n + 1}} and it is shown that any L 0 {L^0} -structure of degree 2 2 over B 2 n + 1 {B_{2n + 1}} can be considered as a contact structure on it. Moreover it is shown that a contact structure can be associated in a canonical way to any contact manifold.