Part I: Transmutations, Integral Equations and Special Functions -- Some Recent Developments in the Transmutation Operator Approach -- Transmutation Operators and Their Applications -- Hankel Generalized Convolutions with the Associated Legendre Functions in the Kernel and Their Applications -- Second Type Neumann Series Related to Nicholson's and to Dixon-Ferrar Formula -- On Some Generalizations of the Properties of the Multidimensional Generalized Erdélyi-Kober Operators and Their Applications -- Alternative Approach to Miller-Paris Transformations and Their Extensions -- Transmutation Operators For Ordinary Dunkl-Darboux Operators -- Theorems on Restriction of Fourier-Bessel and Multidimensional Bessel Transforms to Spherical Surfaces -- Necessary Condition for the Existence of an Intertwining Operator and Classification of Transmutations on Its Basis -- Polynomial Quantization on Line Bundles -- Fourier-Bessel Transforms of Measures and Qualitative Properties of Solutions of Singular Differential Equations -- Inversion of Hyperbolic B-Potentials -- One-Dimensional and Multi-Dimensional Integral Transforms of Buschman-Erdélyi Type with Legendre Functions in Kernels -- Distributions, Non-smooth Manifolds, Transmutations and Boundary Value Problems -- Part II: Transmutations in ODEs, Direct and Inverse Problems -- On a Transformation Operator Approach in the Inverse Spectral Theory of Integral and Integro-Differential Operators -- Expansion in Terms of Appropriate Functions and Transmutations -- Transmutation Operators as a Solvability Concept of Abstract Singular Equations -- On the Bessel-Wright Operator and Transmutation with Applications -- On a Method of Solving Integral Equation of Carleman Type on the Pair of Segments -- Transmutation Operators Boundary Value Problems -- Solution of Inverse Problems for Differential Operators with Delay -- Part III: Transmutations for Partial and Fractional Differential Equations -- Transmutations of the Composed Erdélyi-Kober Fractional Operators and Their Applications -- Distributed Order Equations in Banach Spaces with Sectorial Operators -- Transformation Operators for Fractional Order Ordinary Differential Equations and Their applications -- Strong Solutions of Semilinear Equations with Lower Fractional Derivatives -- Mean Value Theorems and Properties of Solutions of Linear Differential Equations -- Transmutations for Multi-Term Fractional Operators -- Fractional Bessel Integrals and Derivatives on Semi-axes -- The Fractional Derivative Expansion Method in Nonlinear Dynamics of Structures: A Memorial Essay -- Boundary Value Problem with Integral Condition for the Mixed Type Equation with a Singular Coefficient. .