The TolTEC camera is a new millimeter-wave imaging polarimeter designed to fill the focal plane of the 50-m diameter Large Millimeter Telescope (LMT). Combined with the LMT, TolTEC offers high angular resolution (5", 6.3", 9.5") for simultaneous, polarization-sensitive observations in its three wavelength bands: 1.1, 1.4, and 2.0 mm. Additionally, TolTEC is designed to reach groundbreaking mapping speeds in excess of 1 deg2/mJy2/hr, which will enable the completion of deep surveys of large-scale structure, galaxy evolution, and star formation that are currently limited when considering practical observation times for other ground-based observatories. This thesis covers the design as well as the in-lab and LMT characterization of the instrument. Chapter 2 covers TolTEC's design overview and describes each subsystem (cryogenics, optics, detectors, and detector readout). Chapter 3 examines the performance of each subsystem prior to installation at the LMT. In particular, this chapter provides the instrument's responsivity, efficiency, beam response, and readout noise while testing at UMass Amherst. The following chapter covers the initial results from commissioning at the LMT between December 2022 and April 2023. Based on the in-lab testing and LMT commissioning, I provide a number of procedures for operating/repairing the instrument in the appendices. I conclude Chapter 5 with the development of a new pilot study to leverage TolTEC's high resolution and sensitivity with the goal of exploring galaxy cluster thermodynamics across cosmic time. While TolTEC observations of galaxy clusters were not available for this thesis, I describe the analysis pipeline I developed to perform a power spectrum analysis on intracluster medium (ICM) pressure fluctuations. The result of this pipeline is a power spectrum that can be analyzed to extract information on the thermodynamic state of the ICM. This type of study has only been performed on two clusters as of 2023, thus with TolTEC's mapping speed and sensitivity we will be able to expand this study and create the largest sample of its kind.