Jan Maas is Professor at the Institute of Science and Technology Austria (ISTA). He holds a PhD degree from TU Delft and he was a post-doctoral researcher at the University of Warwick and the University of Bonn. He received an ERC Starting Grant in 2016. His research interests are in analysis and probability theory. Simone Rademacher is a researcher in mathematical physics. She received her doctoral degree from the University of Zurich and was a post-doctoral researcher at the Institute of Science and Technology Austria (ISTA). Currently, she is an interim professor at the Ludwig-Maximilians University Munich (LMU). Tamás Titkos is a researcher at the HUN-REN Alfréd Rényi Institute of Mathematics and an associate professor at Corvinus University of Budapest. He holds a PhD degree from Eötvös Loránd University. He is the recipient of the Youth Award and the Alexits Prize of the Hungarian Academy of Sciences. His research interest is in functional analysis. Dániel Virosztek is a research fellow leading the Optimal Transport Research Group of the Rényi Institute. He got his Ph.D. degree in 2016 at TU Budapest and spent four years at the IST Austria as a postdoctoral researcher. He returned to Hungary with a HAS-Momentum grant in 2021. He is working on the geometry of classical and quantum optimal transport.

• Preface.- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli.- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen.- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse.- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan.- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale.- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé.

Jan Maas is Professor at the Institute of Science and Technology Austria (ISTA). He holds a PhD degree from TU Delft and he was a post-doctoral researcher at the University of Warwick and the University of Bonn. He received an ERC Starting Grant in 2016. His research interests are in analysis and probability theory. Simone Rademacher is a researcher in mathematical physics. She received her doctoral degree from the University of Zurich and was a post-doctoral researcher at the Institute of Science and Technology Austria (ISTA). Currently, she is an interim professor at the Ludwig-Maximilians University Munich (LMU). Tamás Titkos is a researcher at the HUN-REN Alfréd Rényi Institute of Mathematics and an associate professor at Corvinus University of Budapest. He holds a PhD degree from Eötvös Loránd University. He is the recipient of the Youth Award and the Alexits Prize of the Hungarian Academy of Sciences. His research interest is in functional analysis. Dániel Virosztek is a research fellow leading the Optimal Transport Research Group of the Rényi Institute. He got his Ph.D. degree in 2016 at TU Budapest and spent four years at the IST Austria as a postdoctoral researcher. He returned to Hungary with a HAS-Momentum grant in 2021. He is working on the geometry of classical and quantum optimal transport.

• Preface.- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli.- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen.- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse.- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan.- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale.- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé.

Jan Maas is Professor at the Institute of Science and Technology Austria (ISTA). He holds a PhD degree from TU Delft and he was a post-doctoral researcher at the University of Warwick and the University of Bonn. He received an ERC Starting Grant in 2016. His research interests are in analysis and probability theory. Simone Rademacher is a researcher in mathematical physics. She received her doctoral degree from the University of Zurich and was a post-doctoral researcher at the Institute of Science and Technology Austria (ISTA). Currently, she is an interim professor at the Ludwig-Maximilians University Munich (LMU). Tamás Titkos is a researcher at the HUN-REN Alfréd Rényi Institute of Mathematics and an associate professor at Corvinus University of Budapest. He holds a PhD degree from Eötvös Loránd University. He is the recipient of the Youth Award and the Alexits Prize of the Hungarian Academy of Sciences. His research interest is in functional analysis. Dániel Virosztek is a research fellow leading the Optimal Transport Research Group of the Rényi Institute. He got his Ph.D. degree in 2016 at TU Budapest and spent four years at the IST Austria as a postdoctoral researcher. He returned to Hungary with a HAS-Momentum grant in 2021. He is working on the geometry of classical and quantum optimal transport.

• Preface.- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli.- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen.- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse.- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan.- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale.- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé.