Lyman $\alpha$ (Ly$\alpha$) emission from star-forming galaxies is an important tool to study a large range of astrophysical questions: it has the potential to carry information about the source galaxy, its nearby circumgalactic medium, and also the surrounding intergalactic medium. Much observational and theoretical work has therefore focused on understanding the details of this emission line. These efforts have been hampered, however, by an absence of spectroscopic reference samples that can be used both as comparisons for observational studies and as critical tests for theoretical work. For this reason we have compiled a large sample of Ly$\alpha$ spectra, at both low and high redshift, and created a publicly available online database, at http://lasd.lyman-alpha.com. The Lyman alpha Spectral Database (LASD) hosts these spectra, as well as large set of spectral and kinematic quantities that have been homogeneously measured for the entire sample. These can easily be viewed online and downloaded in tabular form. The LASD has the capacity for users to easily upload their own Ly$\alpha$ spectra, and all the same spectral measurements will be made, reported, and ingested into the database. We actively invite the community to do so, and the LASD is intended to be a long-term community resource. In this paper we present the design of the database as well as descriptions of the underlying algorithms and the initial Ly$\alpha$ emitter samples that are in the database.