The electrons in the solar wind exhibit an interesting kinetic substructure with many important implications for the overall energetics of the plasma in the heliosphere. We are especially interested in the kinetic evolution of the electron strahl, a field-aligned beam of superthermal electrons, in the near-Sun solar wind. We develop a kinetic transport equation for typical heliospheric conditions based on a Parker-spiral geometry of the magnetic field. We present the results of our theoretical model for the radial evolution of the electron velocity distribution function (VDF) in the solar wind. We study the effects of the adiabatic focusing, free streaming due to the electron temperature gradient, wave-particle interactions, and Coulomb collisions through a generalized kinetic equation for the electron VDF. We compare and contrast our results with the observed effects in the electron VDFs from space missions that explore the radial evolution of electrons in the inner heliosphere such as Helios, Parker Solar Probe, and Solar Orbiter.