1. Introduction
2. Data and sample definition
2.1. Observations and data reduction
2.2. Lyman alpha emitter sample
3. Resolved spectroscopy of the Ly α haloes
3.1. Data binning
3.2. Line extraction and measurements
3.3. Resolved Ly α spectral properties
4. Ly α halo 3D decomposition
4.1. Three-dimensional two-component fits
4.2. Model robustness
5. Spectral characterization of the Ly α emission
5.1. Line parameters
5.2. Halo-Core line profiles comparison
5.3. Halo-Core parameters correlation analysis
5.4. Statistical significance of the spectral differences
6. Connecting host galaxies to their Ly α lines
6.1. Ly α spatial extent and flux
6.2. UV properties of the host galaxy
7. Discussion
7.1. Diversity of the Ly α line profiles in the halo
7.2. Is the Ly α line really broader in the halo?
7.3. New inputs regarding the origin of the Ly α haloes
8. Summary and conclusions