We study intermittent coherent structures in solar wind turbulence from MHD to kinetic plasma scales using Parker Solar Probe data during its first perihelion (at 0.17 au) in the highly Alfvénic slow solar wind. We detect coherent structures using Morlet wavelets. For the first time, we apply a multiscale analysis in physical space. At MHD scales within the inertial range, times scales τ ∈ (1, 10²) s, we find (i) current sheets including switchback boundaries and (ii) Alfvén vortices. Within these events are embedded structures at smaller scales: typically Alfvén vortices at ion scales, τ ∈ (0.08, 1) s, and compressible vortices at sub-ion scales, τ ∈ 8(10^‑3, 10^‑2) s. The number of coherent structures grows toward smaller scales: we observe ∼200 events during a 5 hr time interval at MHD scales, ∼10³ at ion scales, and ∼10⁴ at sub-ion scales. In general, there are multiple structures of ion and sub-ion scales embedded within one MHD structure. There are also examples of ion and sub-ion scale structures outside MHD structures. To quantify the relative importance of different types of structures, we do a statistical comparison of the observed structures with the expectations of models of the current sheets and vortices. The results show the dominance of Alfvén vortices at all scales in contrast to the widespread view of the dominance of current sheets. This means that Alfvén vortices are important building blocks of Alfvénic solar wind turbulence.