Aims. We study the magnetic flux emergence and formation of a sunspot penumbra in the active region NOAA 11024. Methods. We simultaneously observed the Stokes parameters of the photospheric iron lines at 1089.6 nm with the TIP and 617.3 nm with the GFPI spectropolarimeters along with broad-band images using G-band and Ca ii K filters at the German VTT. The photospheric magnetic field vector was reconstructed from an inversion of the measured Stokes profiles. Using the AZAM code, we converted the inclination from line-of-sight (LOS) to the local reference frame (LRF). Results. Individual filaments are resolved in maps of magnetic parameters. The formation of the penumbra is intimately related to the inclined magnetic field. No penumbra forms in areas with strong magnetic field strength and small inclination. corresponds to the merging of one SFP per minute. We also find that, during the formation of the spot penumbra, a) the maximum magnetic field strength of the umbra does not change; b) the magnetic neutral line keeps the same position relative to the umbra; c) the new flux arrives on the emergence side of the spot while the penumbra forms on the opposite side; d) the average LRF inclination of the light bridges decreases from 50• to 37• ; and e) as the penumbra develops, the mean magnetic field strength at the spot border decreases from 1.0 to 0.8 kG.Conclusions. The SFPs associated with elongated granules are the building blocks of structure formation in active regions. During the sunspot formation, their contribution is comparable to the coalescence of pores. Besides a set of critical parameters for the magnetic field, a quiet environment in the surroundings is important for penumbral formation. As remnants of trapped granulation between merging pores, the light bridges are found to play a crucial role in the formation process. They seem to channel the magnetic flux through the spot during its formation. Light bridges are also the locations where the first penumbral filaments form.