The Fermi Large Area Telescope (LAT) has provided the most detailed view to date of the emission towards the Galactic centre (GC) in high-energy γ-rays. This paper describes the analysis of data taken during the first 62 months of the mission in the energy range 1 − 100 GeV from a 15 • × 15 • region about the direction of the GC, and implications for the interstellar emissions produced by cosmic ray (CR) particles interacting with the gas and radiation fields in the inner Galaxy and for the point sources detected. Specialised interstellar emission models (IEMs) are constructed that enable separation of the γ-ray emission from the inner ∼ 1 kpc about the GC from the fore-and background emission from the Galaxy. Based on these models, the interstellar emission from CR electrons interacting with the interstellar radiation field via the inverse Compton (IC) process and CR nuclei inelastically scattering off the gas producing γ-rays via π 0 decays from the inner ∼ 1 kpc is determined. The IC contribution is found to be dominant in the region and strongly enhanced compared to previous studies. A catalog of point sources for the 15 • × 15 • region is self-consistently constructed using these IEMs: the First Fermi-LAT Inner Galaxy point source Catalog (1FIG). The spatial locations, fluxes, and spectral properties of the 1FIG sources are presented, and compared with γ-ray point sources over the same region taken from existing catalogs, including the Third Fermi-LAT Source Catalog (3FGL). In general, the spatial density of 1FIG sources differs from those in the 3FGL, which is attributed to the different treatments of the interstellar emission and energy ranges used by the respective analyses. Three 1FIG sources are found to spatially overlap with supernova remnants (SNRs) listed in Green's SNR catalog; these SNRs have not previously been associated with high-energy γ-ray sources. Most 3FGL sources with known multi-wavelength counterparts are also found. However, the majority of 1FIG point sources are unassociated. After subtracting the interstellar emission and point-source contributions from the data a residual is found that is a sub-dominant fraction of the total flux. But, it is brighter than the γ-ray emission associated with interstellar gas in the inner ∼ 1 kpc derived for the IEMs used in this paper, and comparable to the integrated brightness of the point sources in the region for energies 3 GeV. If spatial templates that peak toward the GC are used to model the positive residual and included in the total model for the 15 • ×15 • region, the agreement with the data improves, but they do not account for all the residual structure. The spectrum of the positive residual modelled with these templates has a strong dependence on the choice of IEM.