Since Gramain wrote the above words in a Seminaire Bourbaki report on classical knot theory in 1976 there have been major advances in 4-dimensional topology， by Casson， Freedman and Quinn. Although a complete classification of 2-knots is not yet in sight， it now seems plausible to expect a characterization of knots in some significant classes in terms of invariants related to the knot group. Thus the subsidiary problem of characterizing 2-knot groups is an essential part of any attempt to classify 2-knots， and it is the principal topic of this book， which is largely algebraic in tone. However we also draw upon 3-manifold theory （for the construction of many examples） and 4-dimensional surgery （to establish uniqueness of knots with given invariants）. It is the interplay between algebra and 3-and 4-dimensional topology that makes the study of 2-knots of particular interest.