Over the last years, several different points of view on p-adic analytic spaces have emerged. This text is devoted specifically to the one that has been introduced by Vladimir G. Berkovich at the end of the eighties, and which has proved one of the most fruitful. We will present several aspects of it. In the first part of the manuscript, we will go beyond the p-adic setting in order to deal with global analytic spaces: those that are defined over Z or ring of integers of number fields. We will prove that they satisfy, at least locally, similar properties as the usual complex analytic spaces. Then, we will turn to the case of p-adic analytic spaces. We will be especially interested in their topology and prove several tameness results. Last, we will show a few applications to p-adic differential equations on analytic curves and explain why their behaviour is controlled by a locally finite graph.
