%0 Journal Article %T Asymptotic Differential Algebra and Model Theory of Transseries %A Matthias Aschenbrenner %A Lou van den Dries %A Joris van der Hoeven %J Mathematics %D 2015 %I arXiv %X We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures. %U http://arxiv.org/abs/1509.02588v1