Carleman Estimates and Unique Continuation for Classical PDE of Second Order
2.1. Main identities and examples
2.2. Carleman estimates for the Laplace operator.  Applications.
2.3. Carleman estimates for the wave operator.  Applications.
2.4. Carleman estimates for the heat and Schrödinger operators.  Applications.

Carleman Estimates for Evolution Operators and Difference Schemes
3.1. Abstract Cauchy problems and Carleman estimates for operators of the first order
3.2. Abstract Cauchy problems and Carleman estimates for operators of the second order
3.3. Carleman estimates for difference schemes

Carleman Estimates for General Differential Operators
4.1. Preliminary results
4.2. Necessary conditions
4.3. Sufficient conditions

Inverse Problems for Hyperbolic Equations
5.1. The one-dimensional case
5.2. Multidimensional inverse problems in the non-characteristic case
5.2. Multidimensional inverse problems in the characteristic case

Inverse Problems for Elliptic, Parabolic, and Schrödinger Equations
6.1. Inverse problems for Schrödinger equations
6.2. Inverse spectral problems for elliptic operators of second order
6.3. Inverse problems of finding unknown part of the boundary or boundary conditions for elliptic equations in the plane
6.4. Inverse problems for parabolic equations