The main research groups working within DMI are the following: evolutionary algorithms; qualitative analysis and stability in thermo-mechanics and bio- mathematics; data mining, clustering and pattern discovery in bio – informatics; variational inequalities and partial differential equations; functional analysis; Traffic Equilibrium Problem in the Continuum case, Time-dependent supernetworks and variational formulations; Lie groups, symmetries and techniques of reduction for partial differential equations; finite geometry, combinatorics, designs theory and graphs and hypergraphs; scientific computing; methods for teaching mathematics; computational methods in bio-mathematics; mathematical models for charge transport in semiconductors; mathematics problems in kinetic theories; multimedia data processing and analysis; theoretical computer science and design methods and criptology; algebraic manifolds; solid mechanics; distributed systems and security; general topology; theory of degenerated elliptic equations; theory of minimax