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This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the WeilDeligne group. For padic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between padic representation theory and geometry on the space of padic representation theory and geometry on the space of padic Langlands parameters. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.
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