1. Basic Mathematical and General Theory.- Regularization and Cross Validation Methods for Nonlinear, Implicit, Ill-posed Inverse Problems.- Active Constraint Strategies in Optimization.- Robust Prediction and an Alternative Iteration Scheme for Ill-posed Problems.- Recovering the Orientation Distribution Function with Maximum Entropy from Experimental Pole Distribution Functions.- Cooperative Approach to Solving Inverse Problems in Integral Geophysics (Theoretical Aspects).- Spherical Spline Approximation and Its Application in Physical Geodesy.- Impedance Scattering Theory and Geophysical Problems.- Boundary Element Analysis of Inverse Problems of Linear Viscoelasticity.- Obtaining Materic Bodies through Concentration and Optimization of a Linear Functional.- The Mellin Transform — Its Properties and Applications in Geophysics.- 2. Gravity and Magnetics.- Optimisation of Magnetic Anomalies via Singular Value Decomposition.- A Statistical Approach to Depth Determination from Gravity Gradients.- Space Domain Iterative Inversion and its Application to the Western Anatolian Grabens.- The Elliptical Current Loop Model of Earth Magnetic and Paleomagnetic Field Sources.- The Influence of the Core-mantle Boundary Irregularities on the Mass Density Distribution Inside the Earth.- The Solution of the Inverse Gravity Problem of the Earth with a Homogeneous Ellipsoid Model.- Stochastic Modelling of Potential Fields for Geological Objects with Complex Internal Structure.- Secular Variation based on Archaeomagnetic Data from Ukraine and Bulgaria.- Can the Geophysical Maps over Buried Ancient Sites Reveal Specific Structures, if Correlated to Predetermined Signals?.- Study of Geomagnetic Field Reversals using the Mellin Transform.- 3. Electrics and Electromagnetics.- A Correlationbetween the Different Models of Resistivity Sounding Data to Discover a New Fresh Water Field in El Sadat City, Western Desert of Egypt.- Fluid Penetration and Formation Temperature Estimation by Inversion of Borehole Measurements.- Interpolation of Induced Polarisation Transients by the Generalized Cole-Cole Relaxation Model.- On the Solution of 2.5D Electromagnetic Field Problems.- 4. Seismics.- Automated Basic Static Corrections.- Fast Radon Transform and Velocity Analysis Applications.- An Optimizational Method for Solving the Inverse Dynamic Problem for the Wave Equation in the Class of Vertically Inhomogeneous Media: Numerical Modeling.- In-depth Parameter for Inversion in Terms of the Type of Stratification.- A Systems Theory Model for Inversion of the Abel Transform.- Numerically-Analytical Method for Calculation of Theoretical Seismograms in Layered-Inhomogeneous Media.- Weighting Factors in the Inversion of Seismic Data.- Algorithm for Calculation of Seismic Wave Field Propagation in the Medium with Curvilinear Free Surface.- Numerical Inversion of Travel Time Observations by Boundary Value Problem Methods.- The Multichannel Constrained Wiener Filter.- 5. Joint Inversion of Geophysical Data and Geothermics.- A Study of the Subsurface Model of Base Metal Mineralization using Complex Geophysical Exploration in Wadi El Khadra Prospect, Kingdom of Saudi Arabia.- Estimation of the Source Model Parameters for Thermal Anomalies in South Silesia.