السلام عليكم ورحمة الله وبركاته
All three groups are part of Ahlus Sunnah wal-Jamaa`ah. They are all three Madhaahib (schools of thought) in `Aqeedah.
Atharis are known as such because they follow the "
Aathaar" (narrations) of the Sahaabah. The differences between the three groups are primarily in the issue of
al-Asmaa was-Sifaat (The Names and Attributes of Allaah Ta`aalaa). Matters such as
Yad, Wajh, Istiwaa, etc. For example,
Yad literally means "Hand". Now, the Atharis say that we are to believe in the Names and Attributes of Allaah Ta`aalaa as they are, without modality. We do not know how the Yad of Allaah Ta`aalaa is, we do not know what is meant by it. We leave the meaning of it up to Allaah Ta`aalaa.
The Ash`ari Madh-hab, founded by Imaam Abu-l Hasan al-Ash`ari, came about originally as a counter measure to the Baatil groups which had sprung up after the
Khayrul Quroon (The Golden Era of Islaam), such as the
Jahmiyyah, Mu`tazaliah, Khawaarij, Murji'ah, etc., and also because of the Greek philosophy which had crept into Muslim ideology. The Ash`aris do
Ta'weel (interpretation) of the
Sifaat. For example, they will say that
Yad means "Power".
Ash`aris and Maatureedis are almost exactly the same. There are only a handful of differences between them.
The Sahaabah
رضوان الله عليهم did not do
Ta'weel of the
Sifaat of Allaah Ta`aalaa. Their way was to leave the meanings of the
Sifaat of Allaah Ta`aalaa up to Him, without delving into them, explaining them, negating them, interpreting them, etc. The Atharis claim to follow the Sahaabah. Whatever
Sifaat of Allaah Ta`aalaa are mentioned in the Qur'aan or in the Ahaadeeth, they believe in without modality (
bilaa kayf).
The four A'immah (Imaam Abu Haneefah, Imaam Maalik, Imaam ash-Shaafi`ee and Imaam Ahmad) were all "Atharis". They lived before the Ash`ari and Maatureedi Madh-habs came into existence.
There are two Kitaabs on `Aqeedah from Imaam Abu Haneefah
رحمة الله عليه himself. They can be downloaded from the following links:
https://archive.org/details/AlFiqhAlAkbar_201606
https://archive.org/details/AlFiqhAlAbsat
There is no need for a person to involve himself in intricate and complex issues. This Kitaab of Imaam Abu Haneefah (i.e.
al-Fiqh al-Akbar) is sufficient. It contains the `Aqeedah of Ahlus Sunnah wal-Jamaa`ah, as espoused by the Sahaabah. I advise you to read it, In Shaa Allaah.
والسلام
