Pirelli has been the Tyre-Partner of F1 since 2011 even though the contract is re-evaluated every three years but the controversy around that is another topic.
Until 2019 they produced 7 slick (dry weather) Tyres called:

ordered by hardness and coloured like the colours of the Tyres

• Superhard 
• Hard [C1]
  
• Medium (white) [C2]
• Soft [C3]
• Supersoft 
• Ultrasoft [C4]
• Hypersoft [C5]

And as you may have noticed, these names were pretty overwhelming. Also, the medium tyre was the hardest tyre to rarely ever be used. So they kicked the Superhard and Supersoft Tyres out and renamed the remaining from C1 to C5, C5 being the softest Tire

But what does the "hardness" of a Tyre mean?
Softer tyres need less heat to work properly and have more grip but the downside is a shorter lifespan, whereas the harder tyres last longer but lack grip, need more heat and therefore more time to get it into the optimal so-called "Tyre-Window".

Back in the day, the drivers could choose their tyres but now Pirelli dictates a set of 3 Compounds (C1-C5) for every weekend but the tyres always have to be related. For Example, C5 can only be used with C4 and C3 and couldn't be used with C1 and C2 so the only possible Tyre variations for a weekend are:

from softest to hardest Compound selection

• C1 - C2 - C3
• C2 - C3 - C4
• C3 - C4 - C5

Each driver then gets 13 sets of dry weather tyres, four sets of intermediates and three sets of full wets.

Intermediates and full wets are self-explaining only for rain and have a special profile to push the water away. That way they lose tons of speed, barely get warm enough and need water to last longer even though they create a dry path on the track. In conclusion: wet tyres are only used in really heavy rain where the dry tyres have no grip and would realistically risk the car just floating off into the Barrier like Carlos Sainz did in Monaco 2023.

Pitstop Strategies are one of the most important factors in modern F1 because cars become widely competitive and get bigger and bigger, making overtaking in general pretty hard. 

So in order to avoid having to overtake everyone on the track or to at least make it much more comfortable, teams use different Pitstop-Strategies. 

This already starts with the Tyre Choice because, as explained above, every type of Tyre lasts a different amount of Laps. As seen with HAAS at the start of the 2024 Canadian GP, the Tyre choice can really make a difference, but still, sooner or later everyone has to pit. However if everyone would Pit about perfectly and at the same Tyre age, nobody would gain any positions. So the teams developed two major Pitstop-Strategies:

1. The "Undercut"
   Execution: A driver pits, before another one to use the fresh Tyres to gain time/space, so that when the other one pits, he will come out after the driver who pitted early, but will not have such a big advantage in terms of Tyre age so he can't easily overtake him back. That way McLarren 'almost' robbed Oscar Piastri of his first F1 Victory at the 2024 Hungarian GP
   Risk: If it's calculated wrong or the Pitstop doesn't go as planned, the driver might end up somewhere in the midfield traffic, having to work hard to even get back to his former position.
2. The "Overcut"
   Execution: Obviously this is the exact opposite, meaning the driver will pit after the expected lap window to sometimes avoid, having to pit several times and to have fresh tyres at the relative end of the race, when everyone else has heavily used tyres. This Strategie is often used under uncertain rain conditions to not wet your fresh tyres and to let the other drivers dry-out the Track.
   The Risk is here, that one might get undercut and if the tyres are used too much, the driver might lose a lot of time to come back from. (And if executed too forced, you might end up too light like George Russel at the 2024 Belgian GP)

To prevent massive incidents, the FIA (Fédération Internationale de l’Automobile) has implemented some Rules on how to overtake. How fairly those are executed is again another topic ;)

First of all, there are three segments on a track that are important for overtaking

1. straights
2. breaking zones for the corner entries and
3. the corner itself

1. General defence on the straights by moving the car left and right is allowed as long as you leave enough space for the attacking car to stay on the road. Unlike Perez did to Magnussen in Monaco 2024 (even though it's always an option to brake as the attacking driver. But not for Magnussen).

In case the leading drivers are catching up to the back end, the overtaking car has to stay on the race line, while the back-end driver has to "move out of the way".

2. The next one is a very common accusation of any driver losing any corner battle. Often cited as "moving under breaking".
This rule says, that the defendant may not move whilst breaking because this could lead to a lock-up of the wheel, which would be potentially dangerous for all involved drivers. Therefore drivers are only allowed to first brake, then steer around the corner. But since every driver brakes and steers differently etc. some drivers use this accusation under absolutely hilarious circumstances (like Verstappen in the 2024 Hungarian GP). 

3. already in the corner, the situation gets a lot more tricky. 
Generally, both cars again have to leave enough space and don't force their opponents off the track. Further on, the attacking car has to make the corner within track limits, so you cannot just speed through it and abuse the run-off area (like Perez accidentally did at the start of the 2024 Miami GP). When overtaking on the inside, the car's front axle has to be aligned with the defending car's mirrors (meaning it has to be slightly ahead), not later than at the Apex of the corner.
When overtaking on the outside line the overtaking car's front Axle only has to align with the defending front axle (so they have to be level)
In both cases, the attacking car has to make the move in a controlled manner. Again, this is referring to both Perez and Verstappen, where this wouldn't be the case.

Parc Fermé (French for "closed park") is a Rule that ensures that the vehicles are set under the supervision of the race control.
This Rule isn't only current in F1 but in almost everything Motorsport Series.

Explicitly, this Rule is supposed to ensure that the F1 teams don't change their cars after the Qualifying, forcing them to make compromises on the car so that it performs in both Qualifying and the race. 

BUT: This rule still allows the team to adjust the settings of their cars. They just can not swap any parts, so no other rear wing or new motor but they may refuel any liquids, gases or adjust the wheel pressure.
P.S. I have to say, I think it is quite funny that in the official FIA Rule Set, there is an extra paragraph (p.48; §40,h,i) saying "Engines may be started". I mean that's quite good to know, otherwise you wouldn't be able to participate at all.

In case a car suffers any damage during Qualifying or the Race, the team is allowed to repair or even swap severely damaged parts with exact copies. When repairing, incidental changes are tolerated.

Generally very important, especially for the track owners to be able to plan for the future, but some are just absolutely horrendous:

• Spa Francochamps (Belgium) - 2025
• Shanghai (China) - 2025
• Monza and Imola (Italy) - 2025
• Mexico-City (Mexico) - 2025
• Monaco (Monaco) - 2025
• Zandvoort (Netherlands) - 2025
• Las Vegas (USA) - 2025
• Baku (Azerbaijan) - 2026
• Caralunya (Spain) - 2026
• Cup of the Americas (USA) - 2026
• Marina Bay (Singapore) - 2028

(Now it's getting horrendous (+5 Years))

• Suzuka (Japan) - 2029
• RedBull Ring (Austria) - 2030
• Interlagos (Brazil) - 2030
• Jeddah (Saudi-Arabia) - 2030
• Abu Dhabi (UAE) - 2030
• Gilles-Villeneuve (Canada) - 2031
• Miami (USA) - 2031
• Hungaroring (Hungary) - 2032
• Losail (Qatar) - 2032
• Silverstone (United Kingdom) - 2034
• Sakhir (Bahrain) - 2036
• Albert Park (Australia) - 2037