The cutting edge of modern physics examines some of the most fundamental questions in science. These questions address the very structure and origin of the universe, the nature of the constituents of all matter and their interactions and the mathematical structures that are necessary for a quantitative formulation of the fundamental laws of nature. Two concrete goals of current focus in fundamental physics are to find a quantum theory of gravity that avoids the inconsistencies that arise from trying to reconcile Einstein's general theory of relativity with quantum mechanics and to find a unified theory which encompasses of all the forces of nature and describes all of the particles which are subject to those forces.

String theory provides a promising candidate for a physical theory that could simultaneously achieve both of these goals. String theory is a physical model which is postulated to describe fundamental interactions at exceedingly small distances where quantum mechanical fluctuations of the geometry of spacetime would become important. As such, it should offer an explanation for the conjectured phenomena which should occur when quantum effects and gravity combine. In fact, string theory has had some spectacular successes in this direction. It has given a microscopic explanation to the apparent thermodynamic properties of black holes and suggested a source of Hawking radiation. It has also been used to understand the structure of some space-time singularities. A current active research area centers on attempting to quantize strings in the background of an expanding universe, possibly with an initial singularity. The goal is to understand whether the microscopic physics described by strings could be imprinted on spacetime in the form of some observable features of the cosmos.

There are solutions of string theory which are tantalizingly similar to the standard model of elementary particle physics which describe the presently observed non-gravitational interactions of elementary particle physics. String theory is the ultimate unification of particles and forces -- the only fundamental object is a string -- different particles are strings with different modes of internal vibration -- and all interactions are simply explained by the splitting and joining of those strings. And, not only does this unify the forces of the standard model in an elegant way, it incorporates gravity in a way which is apparently consistent with quantum mechanics.

As a physical dynamical system, string theory is still not completely understood. It is clear that its full power will only be realized once significant progress has been made in understanding its mathematical and dynamical structure. This will undoubtedly involve the development of radical new physical ideas and new mathematics. This development will be an important frontier area for both mathematics and physics in the foreseeable future.

One of the most interesting features of string theory is duality. Duality is the phenomenon where apparently different theories describe the same dynamics with different mathematical variables. In string theory, dualities take a few different forms. One is duality between different kinds of string theories. It is now known that the five apparently consistent kinds of superstring theory are related by dualities and they are now thought to all be limits of an underlying theory called M-theory. Another example is mirror symmetry, which is currently an active subject of investigation in mathematical string theory. It relates string theories which live on different space-times.

A different kind of duality is holography. It relates string theory living on a particular space-time to an ordinary quantum field theory, usually living on a boundary of the space-time. These later dualities have been used to find string theory duals of various gauge field theories. Being a strong-weak coupling duality, it can give information about either gauge theory or string theory in the strong coupling regime. This subject is currently undergoing vigorous investigation. It promises to progress our understanding of string theories by studying their dual descriptions as field theories. It also yields a string theory dual of the field theories involved and gives a new window for quantitative description of their behaviors.