We have obtained high resolution (R ≈ 220000) - high signal-to-noise (S/N > 500) spectra of 142 field dwarfs of spectral types F–K and v sin i ≤ 45 km s–1. Using the Fourier Transform Method (FTM) we precisely determined rotational velocities (Δ v sin i < 1.0 km s–1). For stars with v sin i ≥ 12.0 km s–1 this method allows the detection of deviations from solid body rotation. In the case of symmetric profiles the differential rotation parameter α = (ωequator – ωpole) / ωequator can be determined. This was possible for 32 of our sample stars; ten stars show evidence for solar-like differential rotation with α > 0.0. Thus it becomes possible to search for connections between differential rotation, rotational velocities and other stellar parameters. Signatures of differential rotation could be found on stars rotating as fast as v sin i = 42 km s–1. Particularly the Li-depleted stars turned out to show strong signatures of differential rotation. Our measurements support the idea, that Li-depletion in fast rotators (v sin i > 15 km s–1) is closely connected to differential rotation.