Hongyu Liu is a Chair Professor of Applied Mathematics at City University of Hong Kong. His research focuses on the analysis, computation and applications of inverse problems and imaging, wave propagation, partial differential equations, mathematical materials science, scattering theory and spectral theory, game theory and mathematical biology.Yi-Hsuan Lin is an Associate Professor of Applied Mathematics at the National Yang Ming Chiao Tung University of Taiwan and a Humboldt Research Fellow of Germany. His research focuses on the analysis, partial differential equations, integro-differential equations, inverse problems, and related topics.

• Preface.- Introduction.- Integro-differential operators.- Part 1. Inverse problems for linear integro-differential operators.- Inverse problems for the fractional Schr¨odinger equation.- Inverse problems for the fractional Schr¨odinger equation with drift.- Inverse problems for variable coefficients nonlocal equations.- Inverse problems for the fractional wave equation.- Part 2. Inverse problems for nonlinear integro-differential operators.- Inverse problems for fractional semilinear elliptic equations.- Montonicity-based inversion formula with power typenonlinearities.- Summary and some open questions.- Bibliography.

Hongyu Liu is a Chair Professor of Applied Mathematics at City University of Hong Kong. His research focuses on the analysis, computation and applications of inverse problems and imaging, wave propagation, partial differential equations, mathematical materials science, scattering theory and spectral theory, game theory and mathematical biology.Yi-Hsuan Lin is an Associate Professor of Applied Mathematics at the National Yang Ming Chiao Tung University of Taiwan and a Humboldt Research Fellow of Germany. His research focuses on the analysis, partial differential equations, integro-differential equations, inverse problems, and related topics.

• Preface.- Introduction.- Integro-differential operators.- Part 1. Inverse problems for linear integro-differential operators.- Inverse problems for the fractional Schr¨odinger equation.- Inverse problems for the fractional Schr¨odinger equation with drift.- Inverse problems for variable coefficients nonlocal equations.- Inverse problems for the fractional wave equation.- Part 2. Inverse problems for nonlinear integro-differential operators.- Inverse problems for fractional semilinear elliptic equations.- Montonicity-based inversion formula with power typenonlinearities.- Summary and some open questions.- Bibliography.

Hongyu Liu is a Chair Professor of Applied Mathematics at City University of Hong Kong. His research focuses on the analysis, computation and applications of inverse problems and imaging, wave propagation, partial differential equations, mathematical materials science, scattering theory and spectral theory, game theory and mathematical biology.Yi-Hsuan Lin is an Associate Professor of Applied Mathematics at the National Yang Ming Chiao Tung University of Taiwan and a Humboldt Research Fellow of Germany. His research focuses on the analysis, partial differential equations, integro-differential equations, inverse problems, and related topics.

• Preface.- Introduction.- Integro-differential operators.- Part 1. Inverse problems for linear integro-differential operators.- Inverse problems for the fractional Schr¨odinger equation.- Inverse problems for the fractional Schr¨odinger equation with drift.- Inverse problems for variable coefficients nonlocal equations.- Inverse problems for the fractional wave equation.- Part 2. Inverse problems for nonlinear integro-differential operators.- Inverse problems for fractional semilinear elliptic equations.- Montonicity-based inversion formula with power typenonlinearities.- Summary and some open questions.- Bibliography.