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Stably stratified fluids, such as stellar and planetary atmospheres, can support and propagate gravity waves. On Earth these waves, which can transport energy and momentum over large distances and can trigger convection, contribute to the formation of our weather and global climate. Gravity waves also play a pivotal role in planetary sciences (e.g. Young et al. 1997) and modern stellar physics (Charbonnel & Talon 2007). They have also been proposed as an agent for the heating of stellar atmospheres and coronae (Mihalas & Toomre 1981), the exact mechanism behind which is one of the outstanding puzzles in solar

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The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere -a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.