On March 28-30, 1996, International Press, the National Science Foundation, and the University of California at Irvine sponsored the First Annual International Press Lecture Series, held on the Irvine campus. The inaugural speaker for this event was Professor Clifford Henry Taubes of Harvard University who delivered three lectures on ""Seiberg-Witten and Gromov Invariants."" In addition, there were ten one-hour lectures delivered by some of the foremost researchers in the field of four dimensional smooth and symplectic topology. Volume I of these proceedings contains articles based on six of those lectures. The present volume consists of four papers by Taubes comprising the complete proof of his remarkable result relating the Seiberg-Witten and Gromov invariants of symplectic four manifolds. The first paper ""SW Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves"" appeared in print in 1996 in the ""Journal of the American Mathematical Society"". The remaining three papers appeared in the ""Journal of Differential Geometry"".
1. SW => Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves; 1. The Seiberg-Witten equations; 2. Estimates; 3. The monotonicity formula; 4. The local structure of [alpha]1(0); 5. Convergence to a current; 6. Positivity and pseudo-holomorphic curves; 7. Constraints on symplectic 4-manifolds; 2. Counting pseudo-holomorphic submanifolds in dimension 4; 1. The definition of Gr; 2. The definition of r(C, 1); 3. The definition of r(C, m) when m > 1; 4. The meaning of the term ""admissable""; 5. The proofs; 6. A toroidal example; 7. D on other surfaces; 3. Gr => SW: From pseudo-holomorphic curves to Seiberg-Witten solutions.