  The aim of this paper is to propose an ``elementary" approach to Coleman's
theory of p-adic abelian integrals. Our main tool is a theory of commutative
p-adic Lie groups (the logarithm map); we use neither dagger analysis nor
Monsky-Washnitzer cohomology theory. Notice that we also treat the case of bad
reduction. A preliminary version of this paper appeared as Expos\'e 9 dans
``Problemes Diophantiens 88-89" (D. Bertrand, M. Waldschmidt), Publ. Math.
Univ. Paris VI 90(1990), 15 pp.
