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Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.

Harmonic analysis -- Congresses. --- Harmonic analysis. --- p-adic groups -- Congresses. --- p-adic groups. --- Representations of Lie groups -- Congresses. --- Representations of Lie groups. --- Lie groups --- p-adic groups --- p-adic analysis --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Lie groups. --- Lie algebras. --- Algebras, Lie --- Groups, Lie --- Mathematics. --- Associative rings. --- Rings (Algebra). --- Topological groups. --- Topological Groups, Lie Groups. --- Associative Rings and Algebras. --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebra, Abstract --- Algebras, Linear --- Topological Groups. --- Algebra. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)