a collection of literature that the course may refer to
Background
Introduction to Differential Topology, lecture notes by J.Robbin and D.SalamonPDEs in Geometry, student-written notes from lectures by D.Salamon
Notes on compact Lie groups, by D.Salamon
Notes on complex Lie groups, by D.Salamon
Gauge Theory Foundations
K.K.Uhlenbeck, Connections with Lp-bounds on curvature, Comm.Math.Phys. 83 (1982)K.K.Uhlenbeck, Removable singularities in Yang-Mills fields, Comm.Math.Phys. 83 (1982)
K.Wehrheim, Uhlenbeck Compactness, EMS Series of Lectures in Mathematics, 2004.
Notes on flat connections and the loop group, by D.Salamon
Yang-Mills/Donaldson theory
S.K.Donaldson, P.B.Kronheimer, The Geometry of Four-manifolds, Clarendon Press, 1990S.K.Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983)
S.K.Donaldson, Polynomial invariants of smooth four-manifolds, Topology 29 (1990)
A. Floer, An instanton invariant for 3-manifolds, Comm. Math. Phys. 118 (1988)
S.K.Donaldson, Floer Homology Groups in Yang-Mills Theory, Cambridge University Press, 2002.
Atiyah-Floer type conjectures
M. F. Atiyah, R. Bott, The Yang Mills equations over Riemann surfaces, Phil.Trans.R.Soc.Lond.A 308 (1982) ; lecture notes by Camilo Arias AbadM.F.Atiyah, New invariants of three and four dimensional manifolds, Proc.Symp.Pure Math. 48 (1988)
C.H.Taubes, Casson’s invariant and gauge theory, J.Diff.Geom. 31 (1990)
S.Dostoglou, D.A.Salamon, Instanton homology and symplectic fixed points, LMS Lecture Notes Series 192, Cambridge University Press, 1993
S.Dostoglou, D.Salamon, Cauchy-Riemann operators, self-duality, and the spectral flow, Birkhaeuser Verlag, Progress in Mathematics, Vol. 119, 1994
S.Dostoglou, D.Salamon, Self-dual instantons and holomorphic curves, Annals of Mathematics 139 (1994) ; Erratum
D.Salamon, Lagrangian intersections, 3-manifolds with boundary, and the Atiyah-Floer conjecture, in Proceedings of the ICM, Zuerich, Birkhaeuser, Basel, 1995
K.Wehrheim, Lagrangian boundary conditions for anti-self-dual instantons and the Atiyah-Floer conjecture, J.Symp.Geom.
D.A.Salamon, K.Wehrheim, Instanton Floer homology with Lagrangian boundary conditions, Geometry & Topology 12 (2008)
Seiberg-Witten Theory
J.W.Morgan, The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds, Princeton University Press, 1995Spin Geometry and Seiberg-Witten Invariants, unfinished manuscript by D.Salamon
D.Salamon, Seiberg-Witten invariants of mapping tori, symplectic fixed points, and Lefschetz numbers, Turkish Journal of Mathematics 23 (1999)
Peter Kronheimer, Tomasz Mrowka, Monopoles and Three-Manifolds, Cambridge University Press, 2007
Symplectic Vortex Equations
K.Cieliebak, A.R.Gaio, D.A.Salamon, J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions, IMRN 10 (2000)K.Cieliebak, A.R.Gaio, I.Mundet i Riera, D.A.Salamon, The symplectic vortex equations and invariants of Hamiltonian group actions, Journal of Symplectic Geometry 1 (2002)