Purity

The Laws of Uncleanliness in the Bible (6 June 2017, 12 Sivan, 5777)

The laws of uncleanness mainly concerned the result of transgression OR ritual purity concerning the Temple.
These laws DO NOT apply to non-Jews but for some of them Jews are still liable.
In the future after the Temple is built and the Ten Tribes have been reconciled it appears that ALL Israelites will have to observe these laws.

Uncleanness in the Biblical Sense entailed contact with the following:

Corpses
Touching or being in the same room as a dead person or coming in contact with a grave.
This meant that if you wished to become pure and enter the Temple area you had to wait seven days, be purified by ritual immersion, spilled on by water mixed with ashes of the red calf, and bring a sacrifice.

Biblical leprosy.
When a leper is healed he must undergo a process of purification that takes at least 7 days.

See:
https://torah.org/learning/halacha-overview-chapter58/

A woman in her menstrual period or other form of discharge.
A man who touched a woman in this state is impure for a day and should undergo a ritual immersion.
If he had intercourse with her it required a seven day period of impurity and the bringing of a sacrifice (Leviticus 15:24).
See:
Leviticus 15:19-30, 18:19, 20:18
The woman when her period had ended had to immerse herself.
These days she waits an additional seven days.
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One Day Waits Followed by Immersion:
The matters below require remaining impure for a day (and not entering the Temple precincts)  followed by ritual immersion in water.

A nocturnal emission or other contact with male semen.

Carrying the carcass of a kosher animal that had died through sickness or been killed in a non-kosher manner.

Touching the dead body of any of the creatures listed in Leviticus 11:29-30, mouse, lizard, etc.
Also someone who eat an unclean animal was unclean,
cf.

Leviticus 11:
 39  Also if one of the animals dies which you have for food, the one who touches its carcass becomes unclean until evening. 40 He too, who eats some of its carcass shall wash his clothes and be unclean until evening, and the one who picks up its carcass shall wash his clothes and be unclean until evening.

Concerning immersion see:
https://torah.org/learning/halacha-overview-chapter63/

Extract:
All of the laws regarding purity and impurity are only on account of sacred things; an impure person is forbidden to enter the Temple or to eat sacred food and offerings, but there is no prohibition as regards the non-sacred. Contact with the impure is permissible, as it says 'Pure and impure together'.5 Nevertheless, it is proper for a pious person to avoid such contact since separation leads to holiness, as it says 'And you shall make yourselves holy and be holy, for I am holy'.6,d