Context. Solar wind evolution differs from a simple radial expansion, while wave-particle interactions are assumed to be the major cause for the observed dynamics of the electron distribution function. In particular, whistler waves are thought to inhibit the electron heat flux and ensure the diffusion of the field-aligned energetic electrons (Strahl electrons) to replenish the halo population. Aims. The goal of our study is to detect and characterize the electromagnetic waves that have the capacity to modify the electron distribution functions, with a special focus on whistler waves. Methods. We carried out a detailed analysis of the electric and magnetic field fluctuations observed by the Solar Orbiter spacecraft during its first orbit around the Sun, between 0.5 and 1 AU. Using data from the Search Coil Magnetometer and electric antenna, both part of the Radio and Plasma Waves (RPW) instrumental suite, we detected the electromagnetic waves with frequencies above 3 Hz and determined the statistical distribution of their amplitudes, frequencies, polarization, and k-vector as a function of distance. Here, we also discuss the relevant instrumental issues regarding the phase between the electric and magnetic measurements as well as the effective length of the electric antenna. Results. An overwhelming majority of the observed waves are right-handed circularly polarized in the solar wind frame and identified as outwardly propagating quasi-parallel whistler waves. Their occurrence rate increases by a least a factor of 2 from 1 AU to 0.5 AU. These results are consistent with the regulation of the heat flux by the whistler heat flux instability. Near 0.5 AU, whistler waves are found to be more field-aligned and to have a smaller normalized frequency (f/f_ce), larger amplitude, and greater bandwidth than at 1 AU.