This slim but very attractive volume contains a write-up of lectures on several important aspects of p-adic analytic geometry and its arithmetic applications. B. Conrad gives an informal introduction into non-Archimedean analytic spaces in their various guises: rigid spaces, their formal models and Berkovich spaces. S. Dasgupta and J. Teitelbaum discuss in great detail the Drinfeld p-adic upper half plane and its relation to p-adic representation theory of GL2(Qp) and the L-invariant of modular forms (the conjecture of Mazur-Tate-Teitelbaum). M. Baker develops potential theory on the Berkovich space attached to the projective line (or more generally to a curve) over a p-adic field. K. Kedlaya gives a crash course on algebraic de Rham and rigid cohomology. This book – which also contains historical reminiscences by J. Tate and V. Berkovich – is highly recommended to PhD students and researchers in arithmetic geometry and related fields.

Reviewer:

jnek