One of the best ways to learn topology is to read the classics. This translation of the 2005 Russian edition include the original methods and constructions from the originals of the 1950s and 1960s. The extended entries include Pontrjagin's article on smooth manifolds and their application in homotopy theory; Thoms' work on global properties of differential manifolds; Novikov's paper on homotropy properties of Tom complexes; papers by Smale on the generalized Poincare's conjecture in dimensions greater than four and the structure of manifolds; Quillen's article on the formal group laws of...

This book consists of a selection of articles devoted to new ideas and develpments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical...