1 Apéritif.- 2 Foundations.- 3 The p -adic Numbers.- 4 Exploring ℚ p .- 5 Elementary Analysis in ℚ p .- 6 Vector Spaces and Field Extensions.- 7 Analysis in ℂ p .- 8 Fun With Your New Head.- A Sage and A (Very) Quick Introduction.- B Hints and Comments on the Problems.- C A Brief Glance at the Literature.- Bibliography.- Index.