This dissertation is about the physics of dilute gaseous Bose-Einstein condensates (BECs) confined to lower dimensions by optical lattices. The central theme of the effects of reduced dimensionality is explored within various one-dimensional (1D) and two-dimensional (2D) systems. We create a 2D BEC by adiabatically increasing the confinement of a trapping potential in one direction to the point where motion in that direction is frozen out. Doing this in two directions, we create a 1D BEC. Two experiments examine the ground state properties of a 1D and 2D system. In the 1D system (Chap. 9), a reduction in three-body recombination signals an increase in correlation resulting in a partial "fermionization" of the Bose gas. In the 2D system (Chap. 8), we measure temperature-dependent condensate phase fluctuations in the vicinity of the Berezinskii-Kosterlitz-Thouless transition.;Other experiments investigate dynamic properties of reduced dimension systems. Strongly inhibited transport of a 1D gas in a lattice is observed in one experiment (Chap. 9). Another 2D experiment measures suppressed collisional decay rates due to the reduced dimensionality (Chap. 9). A final experiment (Chap. 7) examines quantum/classical correspondence in the effectively 1D dynamics of a 3D BEC. The dynamics is effectively 1D in the sense that the experiment is over before motion in the radial directions (which are not frozen out) can occur.;This dissertation also describes the design and implementation of a novel 1D "accordion lattice" (Chaps. 5-6) which greatly facilitated the Berezinskii-Kosterlitz-Thouless experiment, the quantum/classical correspondence experiment, and a "superlattice" experiment conducted to assist in the calibration of the accordion lattice.
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