In this course we intend to give an introduction and review recent developments in nonperturbative aspects of supersymmetric gauge theories.

Accumulation of results obtained in the 1980s culminated in a breakthrough discovery of the Seiberg--Witten solution (1994) in N=2 Yang-Mills theories. This was the first analytic demonstration ever of the dual Meissner effect as the underlying mechanism of color confinement. Since then we witnessed a remarkable progress in understanding non-Abelian string formation and their structure. A full understanding of what happens with the 't Hooft-Polyakov monopoles in the Higgsed theories and how they get confined was achieved.

There are high expectations (supported in part by a number of recent results) that using certain dualities we will be able to pass from confined monopoles to confined quarks in N=1 theories. Dualities going beyond those of Seiberg and Seiberg and Witten were discovered and exploited, with great success, in dealing with various gauge theories at strong coupling. A toolkit was developed which allowed one to obtain a number of elegant exact results.

The tentative plan of the lecture course is:

1. A brief introduction to centrally extended superalgebras;
2. A review of important models with central charges and their implications;
3. Non-Abelian strings; basic bulk gauge theories supporting non-Abelian strings;
4. World-sheet theories on non-Abelian strings;
5. From the 't Hooft-Polyakov monopoles to confined monopoles: a smooth journey without phase transitions;
6. Descending down to N=1 (heterotic non-Abelian strings);
7. Beyond Seiberg-Witten dualities.