Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Tamás Szamuely is a Senior Research Fellow in the Alfréd Rényi Institute of Mathematics at the Hungarian Academy of Sciences, Budapest.

Foreword; 1. Galois theory of fields; 2. Fundamental groups in topology; 3. Riemann surfaces; 4. Fundamental groups of algebraic curves; 5. Fundamental groups of schemes; 6. Tannakian fundamental groups; Bibliography; Index.