The Hydrogen Lyman-alpha (Lya) line, the brightest UV line in high-redshift galaxies, varies in shape due to factors ranging from the interstellar medium to the intergalactic medium. I will present the first systematic inventory and characterisation of the spectral shapes of Lya emission lines from a sample of 468 Lya emitting galaxies (LAEs) between z = 2.8 – 6.6. Using the unprecedented deep GTO data from the MXDF, I developed a method to classify Lya emission lines in four spectral and three spatial categories, by combining a pure spectral analysis with a narrow-band (NB) image analysis. Among the LAE sample cleaned from observational limitations, 51% exhibit double-peaked Lya profiles, a fraction that seems luminosity-dependent. Blue-dominated spectra require systemic redshift measurements from instruments like VLT/KMOS and JWST/NIRSpec to confirm their origin (i.e., from radiative transfer processes or other processes). Looking at the Lya NB images, around 20% of the sample lies in a complex environment, meaning there are other clumps or galaxies at the same redshift within a distance of 30 kpc, which enhances star formation. My results highlight the importance of considering both the spectral and spatial information to interpret Lya lines in galaxies. Statistical samples of double-peaks are promising for studying galaxy evolution. MUSE allows the scientific community to obtain large, unbiased samples along with the necessary spatial and spectral data simultaneously.