Let R be a commutative Noetherian ring, M be a finitely generated R -module and fa be an ideal of R such that fa M neq M. We show among the other things that, if c is a non-negative integer such that H^i_a(M)=0 for all i<c, then there is an isomorphism End(H^c_a(M))=Ext_R^c(H^c_a(M),M); and if c is a non-negative integer‎ such that H^i_a(M)=0 for all i neq c, there are the following isomorphisms: (i) H_b^i(H^c_a(M)) cong H_b^{i+c}(M), and; (ii) Ext_R^i(R/b,H^c_a(M)) cong Ext_R^{i+c}(R/b,M) for all i \\\\in N_0 and all ideals b of R with b \\\\supseteq a. We also prove that if a and b are‎ ideals of R with fb supseteq a and c:=grade(a,M), then there exists a natural homomorphism from End(H^c_a(M)) to End(H^c_b(M)), where grade(a,M) is the maximum length of M-sequences in a.‎

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