Types of Tires
All the tires used in Formula 1. This includes the range of tires that are used in an overall season as well as the types that are used in a race weekend.

Pirelli is the sole provider of tires for Formula 1.
There are two overall groups of tires: slick tires and wet tires. Every race weekend Pirelli chooses a soft, medium and hard tire to bring from their range of 5 types of slick tire.
The soft tire is primarily used in qualifying. It is the softest compound in the lineup which means it's going to be the fastest tire and have the most grip BUT it also has a higher degradation (which means its loses effectiveness and grip). This means they don't last as long.
The medium tire is the middle ground. These tires are slower than the softs but faster than the hards. They also last longer than the softs but shorter than the hards. These tires are usually used during race starts. (Subject to the track)
The last slick tire is the hard tire. They are the most durable but they are also the slowest tire. They can last much longer than the medium or the softs but they wont be as fast as the previous two. They are mainly used during the middle to end of the race.
The level of slick tire that is brought is based on a variety of conditions. This is include the circuit type, track abrasiveness, weather, and speed. These tires are:
C1: The hardest compound of tire. Only used as hard tire allocations. Typically used on hot and abrasive circuits.
C2: Second hardest tire. Primarily used for the Hard or Medium compound. Well suited for faster, hotter & more abrasive circuits
C3: Most versatile compound. Can be used as a hard, medium or soft in a tire selection. Well suited for a range of conditions.
C4: Second softest. Used for the medium or soft compound. Designed for low severity circuits.
C5: The softest tire. Designed for slow circuits with low wear and degradation. Primarily seen at street circuits.
The remaining two kinds of tires are the wet weather tires. These are tires are used in wet conditions.
The intermediate tire is the first level of rain tires. They are used on a wet track with no standing water. They also have treads unlike the slick tires. They are commonly used when rains begins or is ending. They are the faster and preferred tire in wet conditions.
The second tire is the extreme wet tire. These tires are most effective in heavy rain. They have an increased resistance to aquaplaning and allow for drivers to have better grip in extremely wet conditions. You will typically see them used if there are puddles or standing water on the track. Usually if these are needed the race is paused due to weather and unsafe conditions. If a safety care is called due to weather, the drivers wil be required to use these tires.