Purification in Islam
1-Inner Purification
It is the purification of the heart from polytheism, sins etc. It is not possible to attain purification when the filth of polytheism lingers in the heart. As pointed out by Allah I:”O you who believe, verily, the mushrikun (polytheists, pagans, idolaters, disbelievers in oneness of Allah and in the message of Muhammad) are najas (impure). So let them not come near the Al-Masjid Al-Haram (the holy masjid in Makkah) after this year; and if you fear poverty, Allah I will enrich you, if He wills, out of His bounty. Surely, Allah is All-knowing, All-wise.” ( Tawbah:28)
And the Prophet ﷺ said: “Indeed the believer does not become impure.” [ agreed upon by Al-Bukhari and Muslim (This will be referred to as «agreed upon» in the remainder of the book).]
2-Physical Purification
It is the purification of the body from dirt and impurities. Physical purification entails two forms of purification:
1-Purification from Hadath (the state of ritual impurity)
Hadath is that which, when produced from or befalls a body, prevents a Muslim from acts of worship for which purification is a requisite, e.g. As-Salah (prayer), circumambulation of the Ka’abah etc. There are two types of Hadath:
Minor Hadath.. It is that which makes ablution imperative, like urine, defecation, passing wind and all other nullifiers of al-wudu’ (ablution). These will be listed later on in the text. Purification from these is achieved by performing al-wudu’. Allah I says: “O you who believe! When you intend to offer Salah (daily prayer), wash your faces and your hands (forearms) up to the elbows, rub (by passing wet hands over) your heads, and wash your feet up to the ankles. ”(Maidah:6)
Major Hadath .. It is that which makes ghusl (a purificatory bath) imperative, e.g. sexual relations, menstruation etc. Purification from this state is achieved by ghusl. Allah says: “If you are in a state of janabah (i.e. after sexual relations), purify yourselves (by bathing your whole body).” (Maidah:6)
If it is impossible to purify oneself through wudu or ghusl, then one purifies himself through Tayammum (a dry form of purification using soil, to be discussed in a later section).
2-Purification from Najasah (a physical impurity)
Removal of any physical impurity is obligatory, as Allah says: “And purify your garments”(Mudathir: 4).
And the Prophet ﷺ said; “Most of the punishment in the grave is a result of the lack of cleaning (oneself from) urine” [ narrated by Ibn Majah.] and “When any of you comes to the masjid (mosque), he should be mindful of his sandals. If he sees filth or dirt on one (of them), he should wipe it (off) and then (he can) pray in them.” [ narrated by Abu Dawud.]
Purification from physical impurities entails:
1-purification of the place of prayer
2-purification of clothes
3-purification of the body
source: https://www.al-feqh.com/en/purificat...water-in-islam
--------------
All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad 
, is His slave and Messenger.
There are three types of purification:
1- Purification of bodily organs from sins and disobedience:
Allaah Almighty described the polytheists with being unclean. This means that they adopt impure belief, which is polytheism. Allaah says (what means):
• {O you who have believed, indeed the polytheists are unclean.} [Quran 9: 28]
• {Those are the ones for whom Allaah does not Intend to purify their hearts.} [Quran 5: 41]
The Prophet , used to ask Allaah to purify him of sins and disobedience. ‘Abdullaah ibn Abi Awfa 
narrated that the Messenger of Allaah , used to recite (this supplication):
O Allaah! All praise is due to You, filling the heavens, filling the earth, and filling whatever else You Wish. O Allaah! Purify me with snow, (water of) hail and cold water; O Allaah, purify me from sins and misdeeds just as a white garment is cleansed from dirt. [Muslim]
2- Purification from filth:
This includes urine, excrement, blood, liquid alcohol as well as other types of tangible filth. According to the majority of scholars, such filth is purified only by pure water. They must be washed with water until the color, taste and smell of impurity disappear. In case of a dog, a swine as well as what comes from them, this must be washed seven times, including once with dust. The scholars provided different views regarding some details.
3- Purification from ritual impurity:
There are two types:
First: the major impurity: it is a state of impurity which requires Ghusl, as when one releases semen or inserts the tip of the penis into a woman's vagina or a man or woman's anus. Even if there is no ejaculation, both parties are required to perform Ghusl. Also, the woman is required to perform Ghusl at the end of menstruation or post-partum bleeding.
Second: minor impurity: it is a state of impurity which requires Wudhoo’ (ablution), as when something other than semen comes out from the two excretory organs whether it is urine, pre-ejaculatory fluid, excrement, a stone, and so on. This also includes touching one of the two excretory organs with the palm of the hand, whether for himself or for others, unconsciousness due to sleeping, fainting, intoxication, and so on. Touching a sexually desired non-Mahram (permanently unmarriageable) woman (who has attained the age when she is desired by those of sound nature) requires Wudhoo’ according to some scholars. Eating camel flesh also requires Wudhoo’ according to some scholars.
Making Ghusl for Janaabah (state of major impurity due to a wet dream, sexual relations, losing consciousness, ...) requires one’s intention as well as covering the whole body with water. Making Wudhoo’ requires one’s intention and washing the face, the hands up to the elbows, wiping the head and washing the feet up to the ankles.
Allaah Knows best.
http://www.islamweb.net/emainpage/index.php?page=showfatwa&Option=FatwaId&Id=48837
----------------------
https://www.kalamullah.com/Books/en_What_Every_Muslim_Must_Know_about_Purification.pdf
http://islamiclessons.com/wp-content/articles/COR-Tahara-ExplantoryNotes.pdf
https://abdurrahman.org/tahara-purification/
http://islamicmobility.com/pdf/The%20Ritual%20Spiritual%20Purity.pdf
https://www.al-feqh.com/en/purification-of-water-in-islam
https://www.newmuslimguide.com/en/your-purification/57
https://muqith.wordpress.com/2010/01/16/purification-at-taharah/