Just summarize Progress and Poverty, okay. One important note is the "land value" always refers to the undeveloped value of the land. The tax pretends that it's an empty lot with no improvements, taken in the context of its district or neighbourhood. We want the land developed to it's best use, so we make sure not to tax those improvements.
Do land values encourage density, or does density increase land values? It's the productivity of the surrounding society that drives both. Land is valuable because people want to live and work there, and because the land is valuable it makes sense to build up, and as more people live there more culture and services become available, attracting more people. It's a virtuous cycle.
If the rental value of the land is taxed away, the only income a property can generate is based on the rental of the buildings on it. The first order effect is that the stream of rental income is diminished, lowering its value as an asset. Landowners would try to pass the taxes along to their tenants, but the taxes are not evenly distributed on all landowners, so doing so would only drive people renting houses into more land-efficient options and would skew the rental vs ownership decision wildly in favour of ownership.
Because development becomes the only means of generating income from a property, undeveloped property becomes a tax liability instead of being a speculative asset that appreciates over time. Land that had been held out of use enters the market, lowering prices further. This surface-level parking lot in SF's financial district [1] and the thousands like it across North America become something more useful. Because the speculative value of land is being taxed away, land appreciates as its potential for productive use increases, not merely because everyone is buying land because land goes up in value because everyone is buying land.
[1] - https://maps.app.goo.gl/Wtfts56A72BCkmvP8
The more developed a piece of land is, the lower its effective tax rate becomes because the taxable value of the land does not include improvements. This incentivizes development, and disincentivizes sprawl.
gets on soapbox
If you want a small house and a big yard, nobody is telling you that you can't do that, but that's land that other people can't use, and I think that society has more right to tax you for holding a fixed and finite resource for your own use (land value taxes) than it does to tax the the products of your hard work and enterprise (taxes on income, commerce, and property). We want people to use the land wisely so that is some of it for everyone, and we want people to work hard and invest their resources, so why do we tax things exactly the other way around?
It's a multivariate differential field equation. I've summarized it as briefly as I can.