  Asymptotic expansion of the eigenvalues of a Toeplitz matrix with real
symbol. This work provides two results obtained as a consequence of an
inversion formula for Toeplitz matrices with real symbol. First we obtain an
symptotic expression for the minimal eigenvalues of a Toeplitz matrix with a
symbol which is periodic, even and derivable on $[0, 2\pi[$. Next we prove that
a Toeplitz band matrix with a symbol without zeros on the united circle is
invertible with an inverse which is essentially a band matrix. As a consequence
of this last statement we give an asymptotic estimation for the entries of the
inverse of a Toplitz matrix with a regular symbol.
