Cassiopeia A (Cas A) is the youngest known core-collapse supernova remnant in the Galaxy and is perhaps the best-studied supernova remnant in X-rays. Cas A has a line-rich spectrum dominated by thermal emission and, given its high flux, it is an appealing target for high-resolution X-ray spectroscopy. Cas A was observed at two different locations during the Performance Verification phase of the X-ray Imaging and Spectroscopy Mission (XRISM), one location in the south-eastern part of the remnant and one in the north-western part. This paper serves as an overview of these observations and in it we discuss some of the issues relevant for the analysis of the data. We present maps of the so-called spatial-spectral mixing effect due to the fact that the XRISM point-spread function is larger than a pixel in the Resolve calorimeter array. We analyze spectra from two bright, on-axis regions such that the effects of spatial-spectral mixing are minimized. We fit these spectra with a semi-empirical model consisting of two thermal components, a non-thermal component, and a background model. We find that it is critical to include redshifts/blueshifts and broadening of the emission lines in the two thermal components to achieve a reasonable fit, given the high spectral resolution of the Resolve calorimeter. We fit the spectra with two versions of the AtomDB atomic database (3.0.9 and 3.1.0) and two versions of the SPEX (3.08.00 and 3.08.01$^{*}$) spectral fitting software. We report the significant differences in the fitted parameters so that users might understand which results are sensitive to the atomic data version. Overall we find good agreement between AtomDB 3.1.0 and SPEX 3.08.01$^{*}$ for the spectral models considered in this paper. The most significant difference we found between AtomDB 3.0.9 and 3.1.0 and between AtomDB 3.1.0 and SPEX 3.08.01$^{*}$ is the Ni abundance, with the new atomic data favoring a considerably lower (up to a factor of 3) Ni abundance compared with the previous versions. Both regions exhibit significantly enhanced abundances compared to Solar values, indicating that supernova ejecta dominate the emission in these regions. We find that the abundance ratios of ${rm Ti/Fe}$, ${rm Mn/Fe}$, and ${rm Ni/Fe}$ are significantly lower in the north-west than the south-east, with the ${rm Ti/Fe}$ and ${rm Mn/Fe}$ ratios consistent with zero in the north-west. These different abundance ratios from regions on opposite sides of the remnant strengthen the case for an asymmetric explosion of the progenitor. We describe the semi-empirical models that were developed and suggest that they might be useful in the calibration of moderate spectral resolution instruments.
