Introduction	6
	Contents	9
	Part A p-Adic Analysis and Lie Groups	12
	I Foundations	13
	1 Ultrametric Spaces	13
	2 Nonarchimedean Fields	18
	3 Convergent Series	24
	4 Differentiability	27
	5 Power Series	35
	6 Locally Analytic Functions	48
	II Manifolds	54
	7 Charts and Atlases	54
	8 Manifolds	56
	9 The Tangent Space	65
	10 The Topological Vector Space Can (M, E), Part 1	83
	11 Locally Convex K-Vector Spaces	88
	12 The Topological Vector Space Can (M, E), Part 2	93
	III Lie Groups	98
	13 Definitions and Foundations	98
	14 The Universal Enveloping Algebra	110
	15 The Concept of Free Algebras	115
	16 The Campbell-Hausdorff Formula	120
	17 The Convergence of the Hausdorff Series	133
	18 Formal Group Laws	141
	Part B The Algebraic Theory of p-Adic Lie Groups	163
	IV Preliminaries	164
	19 Completed Group Rings	164
	20 The Example of the Group Zpd	170
	21 Continuous Distributions	171
	22 Appendix: Pseudocompact Rings	172
	V p-Valued Pro-p-Groups	175
	23 p-Valuations	175
	24 The Free Group on Two Generators	181
	25 The Operator P	184
	26 Finite Rank Pro-p-Groups	187
	27 Compact p-Adic Lie Groups	198
	VI Completed Group Rings of p-Valued Groups	201
	28 The Ring Filtration	201
	29 Analyticity	207
	30 Saturation	214
	VII The Lie Algebra	224
	31 A Normed Lie Algebra	224
	32 The Hausdorff Series	237
	33 Rational p-Valuations and Applications	248
	34 Coordinates of the First and of the Second Kind	252
	References	256
	Index	258