This might seem odd, but we're going to start with Frostpunk's Law system, rather than eg 'how does harvesting resources work?' or other more basic topics.
So first: the Law framework itself.
In broad strokes, Laws are like a traditional Video Game Tech Tree; you have foundational Laws you can pursue immediately, more 'advanced' Laws locked behind issuing specific other Laws, and issuing Laws provides new tools or alters the behavior of existing tools, with the whole progression heavily gated by time advancement.
The detail-work of the implementation is pretty odd, though.
First of all, where most tech tree systems -including Frostpunk's Workshop tech tree!- have the player select a desired result and then wait some period of time to complete the research, Laws operate 'backwards': you activate a Law, it applies immediately, but then Law selection goes on cooldown for a number of hours based on what Law was just activated.
Second, Laws are completely free and unconstrained by external factors. Laws do not cost resources to pass, the Law cooldown cannot be modified by conditions on the ground, no Law is dependent on an existing research or structure being completed to make the Law possible to pass. (With... one special exception) Only the cooldown, Law tree requirements, and scenario-specific question of when the plot gives access to your secondary Law are relevant.
Third is the factor my feelings are most mixed on: where video game tech trees generally endeavor to have researches be 100% beneficial, the Law system erratically attempts to make Law decisions complicated by them having negative consequences, and/or preventing the passing of a different Law, and/or having the benefit of the Law be itself a trade-off to benefit from. In theory, I find that appropriate to a system of 'lawmaking', but in practice I feel Frostpunk's design would be much better if it had stuck to Laws being clearly beneficial and hinged the design around the aspect of prioritization: which Laws to go for first, no questions about whether a Law should ever be taken.
'Survival' Laws are the starter Laws you always have access to unless you're playing The Last Autumn. (Which has a different tree that will be its own page) I'll be covering these in a somewhat-arbitrary conceptual order, mostly to let me introduce and explain a few other Frostpunk systems I don't really feel deserve a whole page to themselves.
Fighting Arena
Enables the construction of Fighting Arenas. Initiates a quest to build one Fighting Arena within ? days. Failing this quest reduces Hope.
Note that the game doesn't mention the quest. This is actually a pretty annoying thing with Laws that unlock structures: they always trigger a quest to build the structure, they never mention this will happen, and most frustrating of all is that the necessary number of structures is not necessarily 1. Faith has probably the most egregious example of this, but in general it means all of these Laws have an inane 'gotcha' where a first-time player might get in trouble from not budgeting for the structures they will need to build soon because of the game hiding this information. The game does at least let you hover over the building within the Law screen to see its resource cost, but that's only partially helpful to the 'how many will I need?' issue.
As for what the Fighting Arena is about...
img
Costs 15 Wood.
2x2 space
An unmanned structure which slightly reduces Discontent for each person whose housing exists in its radius. No meaningful interaction with temperature.
... well, I have to explain Discontent.