MEGARA (Multi Espectr{o}grafo en GTC de Alta Resoluci{o}n para Astronom{i}a) is an optical (3650~--~9750AA), fibre-fed, medium-high spectral resolution (R = 6000, 12000, 20000) instrument for the GTC 10.4m telescope, commissioned in the summer of 2017, and currently in operation. The scientific exploitation of MEGARA demands a stellar-spectra library to interpret galaxy data and to estimate the contribution of the stellar populations. This paper introduces the MEGARA-GTC spectral library, detailing the rationale behind the catalogue building. We present the spectra of 97 stars (21 individual stars and 56 members of the globular cluster M15, being both sub-samples taken during the commissioning runs; and 20 stars from our on-going GTC Open-Time program). The spectra have R~=~20000 in the HR-R and HR-I setups, centred at 6563 and 8633~AA respectively. We describe the procedures to reduce and analyse the data. Then, we determine the best-fitting theoretical models to each spectrum through a $chi^{2}$ minimisation technique to derive the stellar physical parameters and discuss the results. We have also measured some absorption lines and indices. Finally, this article introduces our project to complete the library and the database to make the spectra available to the community.
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