The concept of a hollow Moon started back in 1901 when HG Wells wrote the novel The First Men in the Moon. Wells, known to many as the Father of Science Fiction, wrote about an epic journey to the Moon. His main characters discovered that the Moon is not what they had expected and that it was, in fact, hollow and inhabited by a strange insect-like alien race. Pretty cool for a novel that was published back in 1901. Still, by the time humans actually visited the Moon over 60 years later, the concept of the Hollow Moon came to the fore again.
So what started this latest theory of a hollow Moon? During the Apollo missions, the astronauts deployed and leave several seismometers in the surface of the Moon. Their purpose was to record movements and vibrations. Over the next several years they were able to receive data about activities on the Moon regularly. These seismometers sent information to the Earth until they were finally switched off as a cost-cutting measure in 1977. These radio transmissions provided a great deal of information about the Moon and its internal structure. One of the main discoveries was the existence of moonquakes. These were classified into four distinct types.
Deep Moonquakes which occurred about 700km beneath the surface. Vibrations which were caused by meteorite impacts, Thermal Quakes and lastly, Shallow Quakes occurring only about 20-30km below the surface. It was the existence of these shallow quakes led to the idea that the Moon may not be as solid as previously thought. In an article that was first written for Popular Science in March 1970, the claim was made that during these shallow quakes made the Moon “ring like a bell.” 
Another related theory is the “Spaceship Moon Theory” which is also known as, the Vasin-Shcherbakov Theory. This theory goes one step further in the concept of a hollow moon and takes it into the realm of pure science fiction. The article published in 1970 by Soviet scientists, hypothesised that the Moon was, in fact, an artificial, hollowed out satellite placed in Earth orbit by unknown beings. Vasin and Shcherbakov were members of the then Soviet Academy of Sciences, but the article was published not in a science journal but in Sputnik, a sort of Soviet Reader’s Digest. In the article, they refused to speculate what type of unknown beings put the artificial satellite in the Earth’s orbit.
This a most unlikely theory surrounding the Moon. SO let us look at some facts about the Moon.
As seen on the image, the Moon like the Earth has a crust, mantle and core. Over the last decade, the Moon was discovered in fact to have a solid Earth-like core. This core is rich in iron and is solid, with a radius of approximately 240 km. The outer primary core is a primarily liquid outer core, with an estimated radius of 320km. The Moon’s core does differ from the Earth’s in that its boundary layer consists of partially molten material with an estimated radius of 480 km. This information was collected using state of the art seismological techniques and applying this to the data taken from the first lunar landings. By doing this NASA was able to make these discoveries.