Aaron Lauda is a professor of mathematics at USC with a joint appointment in physics & astronomy and has a membership in the USC Center for Quantum Information Science and Technology. His research spans representation theory and low-dimensional topology, emphasizing categorification, diagrammatic methods, and higher category theory. He explores links to knot homology, quantum groups, and applications to quantum computation. Marco Marengon received his PhD in 2017 and he is currently a senior research fellow at the Rényi Institute in Budapest. His expertise is in low-dimensional topology, including the topology of smooth 4-manifolds and knot invariants such as Heegaard Floer homology and Khovanov homology. Gordana Matić is a professor of mathematics at the University of Georgia. She has been elected a fellow of the American Mathematical Society in 2015 for her contributions to low-dimensional and contact topology. Her interests are in general in the topology of 3- and 4-manifolds and include contact and symplectic topology, gauge theory and Heegaard Floer homology, smooth surfaces in 4-manifolds and  other related topics András Stipsicz received his PhD in 1994 and currently, he is the director (and a professor) of the Rényi Institute in Budapest. His expertise lies in low dimensional topology, especially in the smooth topology of four-manifolds and invariants of three- and four-manifolds, including Seiberg-Witten and Heegaard Floer invariants. Since 2016, he has been a member of the Hungarian Academy of Sciences.

• Chapter 1. Instanton Floer homologies and applications.- Chapter 2. New quantum invariants from braiding Verma modules.- Chapter 3. An introduction to symplectic geometry and instricption problems.- Chapter 4. Concordance of surfaces in 4-manifolds.- Chapter 5. Constructing locally flat surfaces in 4-manifolds.- Chapter 6. Knotted surfaces in 4-manifolds and their diagrams.- Chapter 7. Link homologies and knotted surfaces.- Chapter 8. Four lectures on smooth four-manifolds.

Aaron Lauda is a professor of mathematics at USC with a joint appointment in physics & astronomy and has a membership in the USC Center for Quantum Information Science and Technology. His research spans representation theory and low-dimensional topology, emphasizing categorification, diagrammatic methods, and higher category theory. He explores links to knot homology, quantum groups, and applications to quantum computation. Marco Marengon received his PhD in 2017 and he is currently a senior research fellow at the Rényi Institute in Budapest. His expertise is in low-dimensional topology, including the topology of smooth 4-manifolds and knot invariants such as Heegaard Floer homology and Khovanov homology. Gordana Matić is a professor of mathematics at the University of Georgia. She has been elected a fellow of the American Mathematical Society in 2015 for her contributions to low-dimensional and contact topology. Her interests are in general in the topology of 3- and 4-manifolds and include contact and symplectic topology, gauge theory and Heegaard Floer homology, smooth surfaces in 4-manifolds and  other related topics András Stipsicz received his PhD in 1994 and currently, he is the director (and a professor) of the Rényi Institute in Budapest. His expertise lies in low dimensional topology, especially in the smooth topology of four-manifolds and invariants of three- and four-manifolds, including Seiberg-Witten and Heegaard Floer invariants. Since 2016, he has been a member of the Hungarian Academy of Sciences.

• Chapter 1. Instanton Floer homologies and applications.- Chapter 2. New quantum invariants from braiding Verma modules.- Chapter 3. An introduction to symplectic geometry and instricption problems.- Chapter 4. Concordance of surfaces in 4-manifolds.- Chapter 5. Constructing locally flat surfaces in 4-manifolds.- Chapter 6. Knotted surfaces in 4-manifolds and their diagrams.- Chapter 7. Link homologies and knotted surfaces.- Chapter 8. Four lectures on smooth four-manifolds.

Aaron Lauda is a professor of mathematics at USC with a joint appointment in physics & astronomy and has a membership in the USC Center for Quantum Information Science and Technology. His research spans representation theory and low-dimensional topology, emphasizing categorification, diagrammatic methods, and higher category theory. He explores links to knot homology, quantum groups, and applications to quantum computation. Marco Marengon received his PhD in 2017 and he is currently a senior research fellow at the Rényi Institute in Budapest. His expertise is in low-dimensional topology, including the topology of smooth 4-manifolds and knot invariants such as Heegaard Floer homology and Khovanov homology. Gordana Matić is a professor of mathematics at the University of Georgia. She has been elected a fellow of the American Mathematical Society in 2015 for her contributions to low-dimensional and contact topology. Her interests are in general in the topology of 3- and 4-manifolds and include contact and symplectic topology, gauge theory and Heegaard Floer homology, smooth surfaces in 4-manifolds and  other related topics András Stipsicz received his PhD in 1994 and currently, he is the director (and a professor) of the Rényi Institute in Budapest. His expertise lies in low dimensional topology, especially in the smooth topology of four-manifolds and invariants of three- and four-manifolds, including Seiberg-Witten and Heegaard Floer invariants. Since 2016, he has been a member of the Hungarian Academy of Sciences.

• Chapter 1. Instanton Floer homologies and applications.- Chapter 2. New quantum invariants from braiding Verma modules.- Chapter 3. An introduction to symplectic geometry and instricption problems.- Chapter 4. Concordance of surfaces in 4-manifolds.- Chapter 5. Constructing locally flat surfaces in 4-manifolds.- Chapter 6. Knotted surfaces in 4-manifolds and their diagrams.- Chapter 7. Link homologies and knotted surfaces.- Chapter 8. Four lectures on smooth four-manifolds.