Motivated to develop quantum technologies and to study ever-more complex quantum systems,scientists are developing increasingly sophisticated experimental tools to control and measure quantum samples such as ensembles of ultracold atoms. A high-finesse optical cavity can be used to measure the state of atoms within its photonic mode with precision limited only by quantum uncertainty. Such a cavity can also be used to mediate interactions between different atoms within the cavity mode. High-resolution microscope objectives have been interfaced with ultracold atom experiments to allow researchers to image single atoms within optical lattices, to trap single atoms in microtweezer arrays, and to imprint arbitrary optical patterns onto atomic ensembles. Among other applications, these technologies have allowed researchers to investigate many-body quantum systems, engineer novel interactions, and realize high-fidelity quantum operations.

This dissertation presents the details of the design, construction, and operation of a new, versatileatomic physics apparatus that combines these two experimental tools. The apparatus includes a high-finesse optical cavity into which atoms are optically transported. In addition, there is a high-numerical-aperture objective aligned to image, with micron-scale resolution, atoms trapped within the center of the optical cavity. We present results demonstrating the capability of this apparatus to deliver and study ultracold atomic samples, ranging from single atoms to Bose-Einstein condensates. We demonstrate a dispersive shift of the cavity resonance due to the presence of atoms in the cavity mode and the trapping and imaging of single atoms in optical microtweezers. We also present an atomic scanning probe microscopy technique with which a single atom in a microtweezer is used to map out the spatial amplitude pattern of an optical cavity mode standing wave by monitoring the position-dependent scattering properties of the atom.