This new 4th volume of mathematical papers of J-P. Serre contains those published between 1985 and 1998 and some unpublished letters. The impact and influence of J-P. Serre's work has been notable ever since his doctoral thesis on homotopy groups: early international recognition of this was manifested in the award of the Fields Medal in 1954. The abundance of deep results and insight contained in his research and survey papers ranging through topology, several complex variables, and algebraic geometry to number theory, group theory, commutative algebra and modular forms, will continue to provide inspiring reading for mathematicians working in these areas, in their research and their teaching. Characteristic of Serre's publications are the many open questions he formulated pointing to further directions of of research. In his 4 volumes of Oeuvres he has provided comments on and corrections to each article, and describes the present status of the open questions with! reference to later results.