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The automorphism group of the Toeplitz C*- algebra,J(C1),generated by Toeplitz operators with C1-symbols on Dirichlet space D is discussed; the K0,K1-groups and the first cohomology group of J(C1) are computed.In addition,the author proves that the spectra of Toeplitz operators with C1-symbols are always connected,and discusses the algebraic properties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and T* = T if and only if T is a scalar operator.