Professor Vitaly D Shafranov is widely known as one of the acknowledged leaders of the world's scientific community in plasma physics and controlled fusion. His theoretical research on plasma equilibrium and stability made an outstanding contribution to the physics of magnetically confined toroidal plasmas which plays a decisive role for the problem of magnetic fusion.Professor Shafranov was born in 1929 in the village of Mordvinovo, Ryazaní Province. He graduated from secondary school in 1946 and, being excited by discussions on the perspectives of the applications of nuclear energy, entered the Physics Department of Moscow State University to specialise in atomic physics. Following graduation in late 1951, he came to the Kurchatov Institute, to academician M A Leontovich, who was recently nominated as head of the theoretical group for controlled fusion research. In the first decade of his work, V D Shafranov had already accomplished theoretical achievements in plasma physics, which are now associated with his name: the Kruskal-Shafranov criterion, the Grad-Shafranov equation, the Shafranov shift (of the toroidal magnetic surfaces) and which outlined that new physical object in the laboratory: the toroidal plasma maintained in equilibrium due to interaction of the toroidal current with the external transverse magnetic field.The first work by V D Shafranov, in co-authorship with M A Leontovich, On the stability of a flexible conductor in the presence of a magnetic field (1952) determined the goal for the experiments initiated by A D Sakharov's proposal on the confinement of a plasma by both the toroidal magnetic field and the inductive electric current, which later led to tokamaks. The approach of that article was improved in the paper On the stability of a cylindrical gaseous conductor in a magnetic field (delivered by L A Artsimovich 1955 6th Int. Symp. Astronomical Union, Stockholm), and in the paper On the stability of a plasma column in the presence of the longitudinal magnetic field and the conducting casing. In these papers the second possible regime of stabilisation by the `frozen' internal longitudinal magnetic field was investigated. Together with S I Braginsky, he also studied the time behaviour of the equilibrium of a high-temperature plasma column in a magnetic field. Several of Shafranov's papers were devoted to the more general problem of the toroidal plasma equilibrium in a magnetic field. In June of 1957, at the 4th International Conference on Ionisation Phenomena in Gases, he presented his paper on an axially symmetric equilibrium equation (now known as the Grad-Shafranov equation), on the virial theorem of the plasma equilibrium in an external magnetic field, and on the formal analogy of such an equilibrium with the toroidal vortex (like the smoke ring) in hydrodynamic flow. In 1958, Shafranov defended his thesis for the degree of Candidate of Science (Russian analogy of PhD), but it immediately earned him the higher scientific degree of a Doctor of Physical and Mathematical Sciences. The results of these investigations were described in Reviews of Plasma Physics 1963 ed M A Leontovich vol 2. His paper on the structure of the collisional shock wave in a plasma is also dated to this period. Some results of this paper were included by Ya B Zelídovich and Yu P Raizer in their book Physics of shock waves and high-temperature hydrodynamic phenomena.A further series of Shafranov's papers from the first decade of his work was related to the propagation and absorption of electromagnetic waves in high-temperature plasma and to certain instabilities. The original approach to the derivation of the dielectric permeability of the plasma from the correlation function of microcurrents, the collisionless absorption of RF waves in a high-temperature plasma, the radiation damping of charged particles in a plasma with magnetic field, and other aspects, formed the basis of his review paper Electromagnetic waves in a plasma in the series Reviews of Plasma Physics 1963 ed M A Leontovich vol 3.In the following years, Shafranov concentrated on developing the theory of plasma equilibrium and stability in toroidal magnetic confinement systems. Together with S I Braginsky, as early as 1958, he prepared a paper (number 2500) on estimations of parameters of the idealised toroidal systems with Ohmic heating for the 2nd International Conference on Peaceful Use of Atomic Energy. These estimates were used for choosing the parameters of the future tokamak T-3. In 1962 he derived the formula for the shift of a toroidal plasma of circular cross-section in a tokamak, which stimulated further improvement of plasma parameters. Later he derived a similar formula for the more complicated case of systems without axial symmetry (e.g. for the figure-eight stellarator with a circular cross-section) and for the circular axis, shearless l = 2 stellarator. He also estimated the influence of the plasma torus curvature on the classical thermal conductivity (1965) and derived (with B B Kadomtsev) the formula for classical diffusion in a tokamak plasma taking into account the drift and pinch effects. He was the first to explain the stability of the tokamak plasma against perturbations with high azimuthal modes (1970) and to give a theory for the determination of certain internal equilibrium parameters in tokamaks by external magnetic measurements. Shafranov's review, written in co-authorship with V S Mukhovatov (Nuclear Fusion 1971), which became a handbook on tokamak systems, was very important for world tokamak research. A more detailed review, in co-authorship with L E Zakharov, on the toroidal plasma equilibrium was presented in Reviews of Plasma Physics 1982 ed M A Leontovich vol 11.The extensive series of papers by Shafranov on plasma equilibrium and stability in the principally steady state toroidal magnetic configurations, both with a rotational transform (stellarators) and without (i.e. with closed magnetic field lines), is essential for the choice of optimal systems for a fusion reactor. His paper Magnetohydrodynamic theory of plasma equilibrium and stability in stellarators: survey of results published in Phys. Fluids 1983, was highly appreciated by those who had been concerned with stellarator research. The most comprehensive review on the theory of stellarators was published, together with V D Pustovitov, in Reviews of Plasma Physics 1984 ed B B Kadomtsev vol 15. An interesting possibility for stabilisation of the MHD instabilities in stellarators by the bootstrap current was discovered together with M I Mikhailov (1989). In the 1990s, V Shafranov concentrated on the innovative stellarator concept associated mainly with the names of A Boozer and J Nuehrenberg. Here, V Shafranov found the invariant vector formulation for the idealised `quasi-symmetry' condition introduced by J Nuehrenberg. The group, headed by Shafranov in his theory department, is now collaborating with various groups working in the field of stellarator system optimisation.The pioneering theoretical research by V D Shafranov on the physics of plasma confinement in toroidal systems, thanks to its depth, clarity and concreteness, has had substantial impact on many physicists, both theorists and experimentalists, throughout the world.V D Shafranov created a strong scientific school of theorists working in the field of magnetic plasma confinement, which is recognised in his own country and abroad. Shafranov is the bright successor of M A Leontovich, and it is only natural that since April 1981 he has been at the head of the Department of Plasma Theory at the Institute of Nuclear Fusion, Kurchatov Institute.In 1981, V D Shafranov was elected a Corresponding Member of the USSR Academy of Sciences. In 1997, he became a full Member of the Academy. For his outstanding contributions to plasma magnetic confinement theory V D Shafranov was awarded the 1971 State Prize of the USSR and the 1984 Lenin Prize.Since 1983 V D Shafranov has served as editor-in-chief of the journal Fizika Plazmy (translated into English as Plasma Physics Reports). In the eighties he edited twelve issues of Plasma Physics in Russian (Moscow: VINITI Publishing), in the series Itogi Nauki i Tekhniki (Recent Progress in Science and Technology in Russian). V D Shafranov is also editor-in-chief of the series Reviews of Plasma Physics (Dordrecht, Germany and New York: Kluwer Academic and Plenum).Professor E P VelikhovPresident of the Kurchatov Institute