A detailed, one-dimensional, time dependend model is presented, describing flame kernel development in spark ignition engines which explicitely accounts for all fundamental properties of the ignition system (supplied electrical energy and power, discharge mode, energy transfer efficiency to spark plasma, plasma temperature distribution, gap width, heat losses to electrodes and chamber walls), of the combustible mixture (pressure, temperature, equivalence ratio, residual gas fraction, laminar burning velocity, type of fuel) and of the flow field (mean flow velocity, turbulence intensity, strain, characteristic time and length scales, flame holder effects). The model is based on the strained flamelet model and predicts kernel growth consistently under virtual all relevant physical/chemical conditions. Model predictions have been verified in extensive studies in an optical engine over a wide range of physical/chemical parameters using advanced optical and laser optical diagnostics. Very good agreement has been obtained between measured and predicted data without a need for adjusting any of the parameters. Four different ranges for flame kernel formation have been identified being governed by the relative magnitudes of plasma velocity, turbulent burning velocity, heat losses, effective strain or flow field effects. The paper describes the derivation of the model, the verification of model predictions against experimental data and the experimental and diagnostic details.