In chapter I, P.A. Meyer1s presentation of local times is briefly recalled, and an independent exposition in the case of continuous martingales is given by J. Azema and M. Yor.

Chapter II is devoted to continuity properties of the local time : conditions are given by M. Yor under which it is continuous in its space parameter ;
J. Walsh develops an interesting example where this fails ; moreover, J. Walsh also studies the continuity properties of the Brownian sheet local time.

Chapter III consists of two very different studies, by N. El Karoui and J. Walsh, who approximate the local time by the downcrossing process.

General reflection problems are solved in Chapter IV by N. El Karoui and M. Chaleyat-Maurel.

D. Ray's theorem on the Markov property of local time is the object of Chapter V : T. Jeulin and M. Yor link this theorem with an unusual representation for certain Brownian variables, J. Walsh with K. Ito's theory of excursion processes.

In Chapter VI, M. Chaleyat-Maurel, Ch. Yoeurp, M. Yor make use of the local time to obtain new results in the study of semi-martingales.