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This is written in a more or less Victorian style - one of the more accessible styles of that age. The story is far from hard SF by modern scientific standards, but I'm not sure what reasonable speculation at the time Wells wrote was. Certainly, there's a great difference between what was known then and now.
The premise of the story is a lone physicist finding a combination of materials that makes a substance which acts as a total insulator for the force of gravity. If you put this substance between an object and the Earth, it is not affected by the Earth's attraction. A sphere is devised which has a number of sections to its surface. Each section has something like Venetian blinds made out of this new substance - making it possible to control whether each section is or is not subject to gravity. In that way the sphere can be attracted by gravity in some directions and free of gravitation in other directions. It's an ingenious way to design a spaceship that does not require fuel of its own - even if today's science tells us it is not possible.
The physicist has been working out in the English countryside. Nearby, a recently bankrupt man, Bedford, has rented a cottage where he hopes to write a play to turn around his fortunes. The story is narrated by Bedford, who makes no pretense of understanding the physics. Bedford is not a bad fellow, but he's not entirely above taking advantage of someone else. Nor is he particularly courageous. Again, he makes little pretense of these facts.
After Bedford meets the physicist and learns the experiments are aimed at finding a substance that would allow objects to be free of gravity, Bedford quickly sees great commercial potential and the promise of huge fortunes. He explains to the physicist, who is surprised and only interested as far as it would benefit humanity. The physicist is more interested in knowledge for its own sake. Bedford joins in the work, leaving behind his play - following his vision of wealth.
The scientist arranges the building of the previously mentioned sphere. He and Bedford take a trip to the Moon in it. It's a considerably different Moon than what we know today. But again there are some interesting ideas with some internal consistency, at least. They land in a desolate crater covered by rocks and a snowy substance. They land there in cold and relative darkness, just before that part of the Moon comes into sunlight. Soon the heat of the sun starts to melt the "snow" - which is actually air that has frozen during the 14 day lunar night. And plants evolved for the extremes of cold and heat of the 14-day days and nights start growing so fast the visitors from Earth can see it happening before their eyes.
Then it turns out there are insectoid Moon men that live underground, but who bring their "cattle" outside during the lunar day. They are captured by the lunar cattle-handlers and taken into the Moon. The Moon's interior is full of caverns, tunnels and wide shafts leading far down into the depths. The physicist hypothesizes there is a sea down at the center of the Moon.
They are imprisoned for a few days. The two Earthlings and these Moon people can't communicate. When the Earthlings are lead out of their cell, the Moon people use cattle prods to get them to go where they want. The prodding provokes Bedford into attacking a Moon man and initiating an escape to the surface. Unfortunately, they have lost their sphere among the fast-growing plants. The lunar night is approaching; they have limited time to find the sphere before they will freeze outside. They split up for their search for the sphere. By the time Bedford finds the sphere, he can only find signs indicating the physicist has been re-captured by the Moon people.
Bedford returns to Earth. It is only much later that radio signals from the Moon are received in which the scientist tells of his stay with the better educated Moon men.
First Men in the Moon must be one of the earliest stories of "first contact" with flesh and blood people of another material world. It explores to some degree issues such as first encountering laborers who are not inclined to see it as an opportunity to communicate with another intelligence, the problem of communicating / language even with more educated / scientific citizens, how the natives may question the visitor's intentions and what to expect from the other species as a whole, and so on. While it may not be entirely convincing, Wells has tried to portray how life might evolve under the extreme conditions of the Moon's 14 day-long period of dark and cold.
After telling his adventures on the Moon, Bedford's narrative seems to draw to a conclusion. Those reading traditional paper books will, presumably, see there are many more pages left in the book. However, those listening to the audio book might simply hear what appears to be an ending and turn off their player. You should continue listening through chapter 26 - or until one hears a message such as "This completes this audiobook"..