This paper introduces a new non-equilibrium topological state, the Floquet topological insulator (FTI), which can be induced in semiconductor quantum wells by applying microwave radiation. The FTI is characterized by the presence of robust helical edge states that are not present in the trivial phase of the system. The velocity of these edge states can be tuned by adjusting the intensity of the microwave radiation. The paper discusses the necessary experimental parameters for realizing this state and highlights the potential applications of FTIs in quantum computing and spintronics. The FTI is defined through the topological properties of the time-independent Floquet operator, which is derived from the periodic time-dependent perturbations applied to the system. The paper demonstrates that periodic perturbations can give rise to new differential operators with topological insulator spectra, leading to chiral edge currents in non-equilibrium systems. The spectral properties of the edge states, such as their velocity and the bandgap of the bulk insulator, can be easily controlled. The paper also discusses the realization of FTIs in HgTe/CdTe quantum wells. By applying a periodic modulation of the Hamiltonian, the system can transition from a trivial phase to a topological phase, resulting in the formation of edge states. The paper shows that the topological properties of the system can be induced via a simple non-equilibrium perturbation in an otherwise topologically trivial system. The paper also explores various methods to realize such a perturbation using experimentally accessible electromagnetic radiation in the microwave-THz regime. The paper discusses the experimental realization of the FTI, considering several options, including the use of a periodic electric field, stress modulation, and magnetic fields. The paper highlights the potential of FTIs in quantum computing and spintronics, as well as their ability to support either co- or counter-propagating helical edge modes. The paper also discusses the symmetry classes of the FTI and the conditions under which the topological properties are preserved. The paper concludes with a discussion of the non-equilibrium onset and steady states of the driven systems, emphasizing the importance of understanding the relaxation mechanisms in the system.This paper introduces a new non-equilibrium topological state, the Floquet topological insulator (FTI), which can be induced in semiconductor quantum wells by applying microwave radiation. The FTI is characterized by the presence of robust helical edge states that are not present in the trivial phase of the system. The velocity of these edge states can be tuned by adjusting the intensity of the microwave radiation. The paper discusses the necessary experimental parameters for realizing this state and highlights the potential applications of FTIs in quantum computing and spintronics. The FTI is defined through the topological properties of the time-independent Floquet operator, which is derived from the periodic time-dependent perturbations applied to the system. The paper demonstrates that periodic perturbations can give rise to new differential operators with topological insulator spectra, leading to chiral edge currents in non-equilibrium systems. The spectral properties of the edge states, such as their velocity and the bandgap of the bulk insulator, can be easily controlled. The paper also discusses the realization of FTIs in HgTe/CdTe quantum wells. By applying a periodic modulation of the Hamiltonian, the system can transition from a trivial phase to a topological phase, resulting in the formation of edge states. The paper shows that the topological properties of the system can be induced via a simple non-equilibrium perturbation in an otherwise topologically trivial system. The paper also explores various methods to realize such a perturbation using experimentally accessible electromagnetic radiation in the microwave-THz regime. The paper discusses the experimental realization of the FTI, considering several options, including the use of a periodic electric field, stress modulation, and magnetic fields. The paper highlights the potential of FTIs in quantum computing and spintronics, as well as their ability to support either co- or counter-propagating helical edge modes. The paper also discusses the symmetry classes of the FTI and the conditions under which the topological properties are preserved. The paper concludes with a discussion of the non-equilibrium onset and steady states of the driven systems, emphasizing the importance of understanding the relaxation mechanisms in the system.