This is a small book on algebra with a focus on the structure of fields. The author discusses polynomial and differential equations and the algebraic structure of their solutions. This text explores many unique and unusual subjects, including constructions with a ruler and compass, the transcendence of pi, and the impossibility of angle trisection.This book is based on notes used by the author over the past two years for a course he taught at the Ecole Polytechnique. There are exercises at the end of each chapter, ranging in difficulty from easy to challenging. To make this book more lively, the author has included pictures of mathematical stamps and mathematicians.

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