In 1994, Witten  introduced a non-linear partial differential equation on a 4-manifold, called the Seiberg-Witten equations today. This PDE has brought significant progresses in 4-dimensional topology and geometry. In this series of lectures, I shall start with the basics of Seiberg-Witten theory and survey some of rather recent developments in Seiberg-Witten theory.
The first lecture is devoted to explain the foundation of Seiberg-Witten theory for closed 4-manifolds and some of classical major applications of it. Most results in this first lecture have been obtained in the last century, but they are explained from a relatively modern viewpoint: more concretely, my exposition shall be based on the technique of finite-dimensional approximations of the Seiberg-Witten equations, along Furuta  and Bauer-Furuta .
In the second lecture, I present what one can say about the diffeomorphism groups of 4-manifolds using Seiberg-Witten theory. This lecture contains much recent study on Seiberg-Witten theory for families of 4-manifolds. I shall explain (perhaps some of) results in [1, 2, 3, 4, 7, 8, 11] of this kind.
The third lecture will be a crash course in Seiberg-Witten Floer homotopy theory, started by Manolescu . Amongst various versions of Floer theory known in low dimensional topology, this theory has a big advantage that one may consider any kind of generalized cohomology theory, such as K-theory. I shall sketch Manolescu's construction of Seiberg-Witten Floer homotopy theory, and explain a recent application in our paper  of this framework to knot theory.
No specific advanced knowledge is needed, but it would be helpful to be familiar with the basics of both of topology and differential geometry.
 David Baraglia, Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants. Algebr. Geom. Topol. 21 (2021), no. 1, 317–349.
 David Baraglia and Hokuto Konno, A gluing formula for families Seiberg-Witten invariants. Geom. Topol. 24 (2020), no. 3, 1381–1456.
 David Baraglia and Hokuto Konno, On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds, arXiv:1903.01649, to appear in J. Topol.
 David Baraglia and Hokuto Konno, A note on the Nielsen realization problem for K3 surfaces, arXiv:1908.03970, to appear in Proc. Amer. Math. Soc.
 Stefan Bauer and Mikio Furuta, A stable cohomotopy refinement of Seiberg-Witten invariants. I, Invent. Math. 155 (2004), no. 1, 1–19.
 Mikio Furuta, Monopole equation and the 11/8-conjecture, Math. Res. Lett. 8 (2001), no. 3, 279–291.
 Tsuyoshi Kato, Hokuto Konno, and Nobuhiro Nakamura, Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds. Compos. Math. 157 (2021), no. 4, 770–808.
 Hokuto Konno, Masaki Taniguchi, The groups of diffeomorphisms and homeomorphisms of 4-manifolds with boundary, arXiv:2010.00340
 Hokuto Konno, Jin Miyazawa, and Masaki Taniguchi, Involutions, knots, and Floer K-theory, arXiv:2110.09258
 Ciprian Manolescu, Seiberg-Witten-Floer stable homotopy type of three-manifolds with b1=0. Geom. Topol. 7 (2003), 889–932.
 Daniel Ruberman, An obstruction to smooth isotopy in dimension 4. Math. Res. Lett. 5 (1998), no. 6, 743–758.
 Edward Witten, Monopoles and four-manifolds. Math. Res. Lett. 1 (6):769–796, 1994.
Lecture 1 2022.03.16.pdf Lecture 2 2022.03.24.pdf Lecture 3 2022.03.28.pdf