Lunar seismology

Lunar seismology is the study of ground motions of the Moon and the events, typically impacts or moonquakes, that excite them.
History.
Several seismographic measuring systems have already been installed on the Moon and their data made available to scientists (such as those from the Apollo Lunar Surface Experiments Package).
The existence of moonquakes was an unexpected discovery from seismometers placed on the Moon by Apollo astronauts from 1969 through 1972. The Apollo 11 instrument functioned through August of the landing year. The instruments placed by the Apollo 12, 14, 15, and 16 missions were functional until they were switched off in 1977. Moonquakes are not believed to be caused by tectonic plate movement (as earthquakes are), but by tidal forces between Earth and the Moon. Further data is needed to clarify the origins and effects of the forces causing moonquakes.
Major findings.
Moonquakes.
Several categories of moonquakes were recorded. Hundreds of deep moonquakes were recorded along with 28 shallow events. The deeper quakes are caused by tidal forces with the Earth and tended to occur in clusters. The shallow events have tectonic origins. Although more rare than deep events, the shallow events were larger, with body wave magnitudes > 5.5 and stress drops exceeding 100 MPa. 
Other sources of seismic activity included meteorite impacts and artificial signals from lunar modules.
Structure of the Lunar Interior.
One key finding was an improved understanding of the structure of the deep lunar interior, including the existence of a solid inner-core and sharp core-mantle boundary and a partial-melt layer at the base of the lunar mantle. The solid core has a radius of about 240 km and is surrounded by a much thinner liquid outer core with a thickness of about 90 km. The partial melt layer sits above the liquid outer core and has a thickness of about 150 km. The mantle extends to within 45 ± 5 km of the lunar surface.
Future plans.
Due to the success of the Apollo seismometers, several space agencies including NASA have expressed interest in funding future seismic missions to the Moon. NASA's Planetary Science Decadal Survey for 2012-2022 lists a lunar geophysical network as a recommended New Frontiers mission. The mission would be tasked with enhancing the knowledge of the lunar interior using several identical landers distributed over the lunar surface. A network of arrays would be able to better constrain lunar seismicity, especially on the far side of the Moon.
In early 2018, NASA a new program called the Development and Advancement of Lunar Instrumentation (DALI). The goal of DALI is to fund potential instruments so that they reach a technology readiness level of 6, meaning the instruments could be proposed for flight opportunities as early as 2023 and would not require significant technology development. DALI looks to fund instruments that would support the Science Mission Directorate's Planetary Science Division, including the desired lunar geophysical network. The due-date for proposals was in the Spring of 2018, and selected proposals were not announced as of September 2018.