Abstract: The aim of present talk is to introduce topological solitons in field theory and string theory. First classical solitons history and the way they entered physics is reviewed.
To start the subject of topological solitons, first the conditions that these solitons appear are discussed and then solitons of different dimension are introduced. Discussion includes solitons in one spatial dimension (kinks), two spatial dimensions (vortices) and three spatial dimensions (monopoles).
Solitons of four dimensional Euclidean space are called instantons. Reasons for making the space Euclidean will be given and then instantons in QCD will be discussed. As an application of instanton effects, its contribution to the parton distribution function, in a qualitative manner will be presented.
Because one of the important applications of supersymmetry is in soliton formalism, after some introduction to the subject, BPS solitons will be introduced.
Finally solitons in string theory will be discussed. With the introduction of black holes as gravitational solitons, the role of black branes in supergravity is mentioned. After introducing the concept of dualities and the point that supergravities are low energy limit of string theories, D-branes are introduced as solitons of string theory. Some of the implications of the concept of D-branes will be discussed. As one of the important implications of solitons in strin theory, one of the most stringent method of testing Ads/CFT will be discussed in brief.