Alternative Pseudodifferential Analysis : With an Application to Modular Forms Preface Introduction The Metaplectic and Anaplectic Representations The One dimensional Alternative Pseudodifferential Analysis From Anaplectic Analysis to Usual Analysis Pseudodifferential Analysis and Modular Forms Index Bibliography. This volume introduces an entirely new pseudodifferential analysis on the line the opposition of which to the usual (Weyl type) analysis can be said to reflect that in representation theory between the representations from the discrete and from the (full non unitary) series or that between modular forms of the holomorphic and substitute for the usual Moyal type brackets. This pseudodifferential analysis relies on the one dimensional case of the recently introduced anaplectic representation and analysis a competitor of the metaplectic representation and usual analysis. Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms the book may also appeal to analysts and physicists for its concepts making possible the transformation of creation annihilation operators into automorphisms simultaneously changing the usual scalar product into an indefinite but still non degenerate one.