Understanding galaxy evolution is central to astrophysics, with high-redshift Lyman-alpha emitters (LAEs) offering critical insights into the early Universe. The Lyman-alpha (Lya) emission line is a key observational tool, though its interpretation is complicated by radiative transfer effects. This thesis presents the development of an unbiased, automated method to classify the spectral and spatial diversity of Lya line profiles in a blind sample of nearly 500 LAEs spanning a wide high-redshift range, using deep data from the MUSE instrument on the VLT. The analysis reveals a striking variety in Lya shapes, with nearly half exhibiting double-peaked profiles. These are linked to both outflows and previously underreported inflows. A subset may also leak Lyman-continuum photons, relevant for cosmic reionisation. These results highlight the importance of accurate systemic redshifts and spatial diagnostics, challenging prior methodologies and advancing a more comprehensive understanding of LAEs and their role in galaxy formation.