This work presents some classical as well as some very recent results and techniques concerning the spectral geometry corresponding to the Laplace-Beltrami operator and the Hodge-de Rham operators. br/ It treats many topics that are not usually dealt with in this field, such as the continuous dependence of the eigenvalues with respect to the Riemannian metric in the CINFINITY-topology, and some of their consequences, such as Uhlenbeck's genericity theorem; examples of non-isometric flat tori in all dimensions greater than or equal to four; Gordon's classical techniqu
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