Lyman {alpha} blobs (LABs) are large-scale radio-quiet Lyman {alpha} (Ly{alpha}) nebula at high-z that occur predominantly in overdense proto-cluster regions. In particular, there is the prototypical SSA22a-LAB1 at z=3.1 which has become an observational reference. We want to understand the powering mechanisms that drive the LAB so that we may gain empirical insights into the galaxy-formation processes within a rare dense environment at high-z. Thus, we need to infer the distribution, the dynamics, and the ionisation state of LAB 1's Ly{alpha} emitting gas. LAB 1 was observed for 17.2h with the VLT/MUSE integral-field spectrograph. We produced optimally extracted narrow band images, in Ly{alpha} {lambda}1216, HeII {lambda}1640, and we tried to detect CIV {lambda}1549 emission. By utilising a moment-based analysis, we mapped the kinematics and the line profile characteristics of the blob. We also linked the inferences from the line profile analysis to previous results from imaging polarimetry. We map Ly{alpha} emission from the blob down to surface-brightness limits of ~6x10^-19^erg/s/cm^2^/arcsec^2^. At this depth, we reveal a bridge between LAB 1 and its northern neighbour LAB 8, as well as a shell-like filament towards the south of LAB 1. The complexity and morphology of the Ly{alpha} profile vary strongly throughout the blob. Despite the complexity, we find a coherent large-scale east-west velocity gradient of ~1000km/s that is aligned perpendicular to the major axis of the blob. Moreover, we observe a negative correlation of Ly{alpha} polarisation fraction with Ly{alpha} line width and a positive correlation with absolute line-of-sight velocity. Finally, we reveal HeII emission in three distinct regions within the blob, however, we can only provide upper limits for CIV. Various gas excitation mechanisms are at play in LAB 1: ionising radiation and feedback effects dominate near the embedded galaxies, while Ly{alpha} scattering contributes at larger distances. However, HeII/Ly{alpha} ratios combined with upper limits on CIV/Ly{alpha} are not able to discriminate between active galactic nucleus (AGN) ionisation and feedback-driven shocks. The alignment of the angular momentum vector parallel to the morphological principal axis appears to be at odds with the predicted norm for high-mass halos, but this most likely reflects that LAB 1 resides at a node of multiple intersecting filaments of the cosmic web. LAB 1 can thus be thought of as a progenitor of a present-day massive elliptical within a galaxy cluster.