Electric dipole spin resonance is the electron spin resonance driven by a resonant AC electric field E ~ ~ . Because the Compton length λ λ C = ℏ ℏ / m c ≈ ≈ 4 × × 10 − − 11 c m , entering into the Bohr magneton μ μ B = e λ λ C / 2 and controlling the coupling of electron spin to AC magnetic field B ~ ~ , is much shorter than all characteristic lengths of solid state physics, EDSR can be by orders of magnitude stronger than EPR driven by an AC magnetic field. EDSR is usually strongest in materials without the inversion center where the two-fold degeneracy of the energy spectrum is lifted and time-symmetric Hamiltonians include products of the spin related Pauli matrices σ σ , as S = ( ℏ ℏ / 2 ) σ σ , and odd powers of the crystal momentum k . In such cases electron spin is coupled to the vector-potential A ~ ~ of electromagnetic field. Remarkably, EDSR on free electrons can be observed not only at the spin-resonance frequency ω ω S but also at its linear combinations with the cyclotron resonance frequency ω ω C . In narrow-gap semiconductors with inversion center EDSR can emerge due direct coupling of electric field E ~ ~ to the anomalous coordinate r S O .