Differential algebraic function field of one variable -- Movable singularities -- Fuchs' theorem -- Extensions of the coefficient field -- Briot-Bouquet's theorem -- Clairaut fields -- Poincarรฉ fields -- Analogs of addition formulae for elliptic functions -- Poincarรฉ fields generated by the constants -- Poincarรฉ fields of characteristic 0 -- Automorphisms of an elliptic field -- Differential automorphisms -- Differential automorphisms of a Poincarรฉ field -- Riccati fields of characteristic 0 -- Weierstrass points -- Clairaut fields of characteristic 0 -- Movable singularities in case of characteristic 0 -- Differential Lefschetz principle